Prokopenko, M, Harré, M, Lizier, J, Boschetti, F, Peppas, P & Kauffman, S 2019, 'Self-referential basis of undecidable dynamics: From the Liar paradox and the halting problem to the edge of chaos', Physics of Life Reviews.View/Download from: Publisher's site
© 2019 In this paper we explore several fundamental relations between formal systems, algorithms, and dynamical systems, focussing on the roles of undecidability, universality, diagonalization, and self-reference in each of these computational frameworks. Some of these interconnections are well-known, while some are clarified in this study as a result of a fine-grained comparison between recursive formal systems, Turing machines, and Cellular Automata (CAs). In particular, we elaborate on the diagonalization argument applied to distributed computation carried out by CAs, illustrating the key elements of Gödel's proof for CAs. The comparative analysis emphasizes three factors which underlie the capacity to generate undecidable dynamics within the examined computational frameworks: (i) the program-data duality; (ii) the potential to access an infinite computational medium; and (iii) the ability to implement negation. The considered adaptations of Gödel's proof distinguish between computational universality and undecidability, and show how the diagonalization argument exploits, on several levels, the self-referential basis of undecidability.
© 2019, Springer Nature Switzerland AG. In this article, we provide the epistemic-entrenchment and partial-meet characterizations of a new, important class of concrete revision operators (all of which satisfy the AGM postulates for revision), called Parametrized Difference revision operators (PD operators, for short). PD operators are natural generalizations of Dalal's revision operator, with a much greater range of applicability, hence, the epistemic-entrenchment and partial-meet characterizations of the latter are also provided, as a by-product. Lastly, we prove that PD operators satisfy the strong version of Parikh's relevance-sensitive axiom for belief revision, showing that they are fully compatible with the notion of relevance.
© 2018 ACM. In artificial intelligence, a key question concerns how an agent may rationally revise its beliefs in light of new information. The standard (AGM) approach to belief revision assumes that the underlying logic contains classical propositional logic. This is a significant limitation, since many representation schemes in AI don't subsume propositional logic. In this article, we consider the question of what the minimal requirements are on a logic, such that the AGM approach to revision may be formulated. We show that AGM-style revision can be obtained even when extremely little is assumed of the underlying language and its semantics; in fact, one requires little more than a language with sentences that are satisfied at models, or possible worlds. The classical AGM postulates are expressed in this framework and a representation result is established between the postulate set and certain preorders on possible worlds. To obtain the representation result, we add a new postulate to the AGM postulates, and we add a constraint to preorders on worlds. Crucially, both of these additions are redundant in the original AGM framework, and so we extend, rather than modify, the AGM approach. As well, iterated revision is addressed and the Darwiche/Pearl postulates are shown to be compatible with our approach. Various examples are given to illustrate the approach, including Horn clause revision, revision in extended logic programs, and belief revision in a very basic logic called literal revision.
Reis, MDL, Peppas, P & Ferme, E 2016, 'Two axiomatic characterizations for the system of spheres-based (and the Epistemic Entrenchment-based) multiple contractions', ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE, vol. 78, no. 3-4, pp. 181-203.View/Download from: UTS OPUS or Publisher's site
Reis, MDL, Ferme, E & Peppas, P 2016, 'Construction of system of spheres-based transitively relational partial meet multiple contractions: An impossibility result', ARTIFICIAL INTELLIGENCE, vol. 233, pp. 122-141.View/Download from: UTS OPUS or Publisher's site
Possible-world semantics are provided for Parikh's relevance-sensitive axiom for belief
revision, known as axiom (P). Loosely speaking, axiom (P) states that if a belief set K
can be divided into two disjoint compartments, and the new information φ relates only
to the first compartment, then the second compartment should not be effected by the
revision of K by φ. Using the well-known connection between AGM revision functions and
preorders on possible worlds as our starting point, we formulate additional constraints on
such preorders that characterise precisely Parikh's axiom (P). Interestingly, the additional
constraints essentially generalise a criterion of plausibility between possible worlds that
predates axiom (P). A by-product of our study is the identification of two possible readings
of Parikh's axiom (P), which we call the strong and the weak versions of the axiom.
Regarding specific operators, we show that Dalal's belief revision operator satisfies both
weak and strong (P), and it is therefore relevance-sensitive.
In a recent article, Zhang and Foo generalized the AGM postulates for contraction to include infinite epistemic input. The new type of belief change is called set contraction. Zhang and Foo also introduced a constructive model for set contraction, called nicely ordered partition, as a generalization of epistemic entrenchment. It was shown however that the functions induced from nicely ordered partitions do not quite match the postulates for set contraction. The mismatch was fixed with the introduction of an extra condition called the limit postulate. The limit postulate establishes a connection between contraction by infinite epistemic input and contraction by finite epistemic input (reducing the former to the latter) and it is appealing both on mathematical and on conceptual grounds. It is debatable however whether the limit postulate can be adopted as a general feature of rationality in set contraction. Instead we propose that the limit postulate is viewed as a condition characterizing an important special case of set contraction functions. With this reading in mind, in this article we introduce an alternative generalization of epistemic entrenchment, based on the notion of comparative possibility. We prove that the functions induced from comparative possibility preorders precisely match those satisfying the postulates for set contraction (without the limit postulate). The relationship between comparative possibility and epistemic entrenchment is also investigated. Finally, we formulate necessary and sufficient conditions under which the functions induced from comparative possibility preorders coincide with the special class of contraction functions characterized by the limit postulate.
Multiple Belief Change extends the classical AGM framework for Belief Revision introduced by Alchourron, Gardenfors, and Makinson in the early '80s. The extended framework includes epistemic input represented as a (possibly infinite) set of sentences, as
Koutras, CD, Nomikos, C & Peppas, P 2008, 'On a simple 3-valued modal language and a 3-valued logic of 'not-fully-justified belief', Logic Journal of the IGPL, vol. 16, no. 6, pp. 591-604.View/Download from: Publisher's site
In this paper, we advocate the usage of the family of Heyting-valued modal logics, introduced by M. Fitting, by presenting a simple 3-valued modal language and axiomatizing an interesting 3-valued logic of belief. We give two simple bisimulation relations for the modal language, one that respects non-falsity and one that respects the truth value. The doxastic logic axiomatized, apart from being interesting in its own right for KR applications, (i) it comes with an underlying 3-valued propositional logic which is a syntactic variant of the 'logic of here-and-there', whose importance in KR and Logic Programming is well-known, (ii) it is endowed from its very inception with a Gentzen-style proof theory from [Fit92] and a completeness theorem from [KNP02], (iii) it can be equivalently seen as a logic describing the epistemic agreement of two interrelated agents: a K45 agent who 'dominates' an S5 agent, (iv) as we show here, its satisfiability problem is NP-complete, i.e. at the lower level one can expect for applied logics. This is the first concrete example of an epistemic logic from Fitting's framework, that has been overlooked hitherto, despite its many attractive characteristics.
Stavrinoudis, D, Xenos, M, Peppas, P & Christodoulakis, D 2005, 'Early estimation of users' perception of software quality', Software Quality Journal, vol. 13, no. 2, pp. 155-175.View/Download from: Publisher's site
This paper presents a methodology for estimating users' opinion of the quality of a software product. Users' opinion changes with time as they progressively become more acquainted with the software product. In this paper, we study the dynamics of users' opinion and offer a method for assessing users' final perception, based on measurements in the early stages of product release. The paper also presents methods for collecting users' opinion and from the derived data, shows how their initial belief state for the quality of the product is formed. It adapts aspects of Belief Revision theory in order to present a way of estimating users' opinion, subsequently formed after their opinion revisions. This estimation is achieved by using the initial measurements and without having to conduct surveys frequently. It reports the correlation that users tend to infer among quality characteristics and represents this correlation through a determination of a set of constraints between the scores of each quality characteristic. Finally, this paper presents a fast and automated way of forming users' new belief state for the quality of a product after examining their opinion revisions. © 2005 Springer Science + Business Media, Inc.
In his seminal paper in 1988, Grove provided possible-world semantics for the axiomatic approach to belief revision proposed by Alchourron, Gardenfors, and Makinson. Grove's semantics are based on a system of spheres, which is essentially a total preorder on possible worlds, satisfying a particular smoothness condition called the limit assumption. In this article we build upon Grove's representation result working in two (related) directions. In particular, the first part of the article considers a number of smoothness conditions (variants of the limit assumption) as additional constraints to systems of spheres, and studies their implications for AGM belief revision. Such smoothness conditions are of particular importance in the context of multiple revision, that is, revision with respect to a (possibly infinite) set of sentences. In the second part of the article we examine closely this process and, in the spirit of Grove, we provide a constructive model for multiple revision based on systems of spheres and prove the corresponding representation result. Finally, we examine ways of reducing multiple revision to classical AGM sentence revision, and we devise a particular smoothness condition which is shown to be necessary and sufficient for such a reduction.
Koutras, C, Gaga, A & Peppas, P 2004, 'Conciseness considerations on logics of action', Journal of Intelligent Systems, vol. 13, no. 1, pp. 71-94.
In recent years a number of formal results have been established on the correctness of some well-known logics of actions. Correctness however is only one side of the coin; for a theory of action to qualify as a solution to the frame problem, the conciseness of its representations is also relevant. In a previous paper (Peppas et al., 2001) we developed a general framework within which logics of action can be assessed both in terms of correctness as well as conciseness. Herein we apply the results obtained in that paper to evaluate the logic of action proposed by Kartha and Lifschitz (1994).
The AGM approach to belief change is not geared to provide a decent account of iterated belief change. Darwiche and Pearl have sought to extend the AGM proposal in an interesting way to deal with this problem. We show that the original Darwiche-Pearl approach is, on the one hand excessively strong and, on the other rather limited in scope. The later Darwiche-Pearl approach, we argue, although it addresses the first problem, still remains rather permissive. We address both these issues by (1) assuming a dynamic revision operator that changes to a new revision operator after each instance of belief change, and (2) strengthening the Darwiche-Pearl proposal. Moreover, we provide constructions of this dynamic revision operator via entrenchment kinematics as well as a simple form of lexicographic revision, and prove representation results connecting these accounts. © 2003 Elsevier Science B.V. All rights reserved.
Tselekidis, G, Peppas, P & Williams, M 2003, 'Belief revision and organisational knowledge dynamics', Journal Of The Operational Research Society, vol. 54, no. 9, pp. 914-923.View/Download from: UTS OPUS or Publisher's site
Koutras, CD & Peppas, P 2002, 'Weaker axioms, more ranges', Fundamenta Informaticae, vol. 51, no. 3, pp. 297-310.
In the family of many-valued modal languages proposed by M. Fitting in 1992, every modal language is based on an underlying Heyting algebra which provides the space of truth values. The lattice of truth values is explicitly represented in the language by a set of special constants and this allows for forming weak, generalized, many-valued analogs of all classical modal axioms. Weak axioms of this kind have been recently investigated from the canonicity, completeness and correspondence perspective. In this paper, we provide some results on the effect of adopting weak versions of the axioms D, T, 4, 5 and w5 in the family of many-valued modal non-monotonic logics, à la McDermott and Doyle, introduced in  and further investigated in . For many-valued modal languages built on finite chains, we extend the results of  by proving two quite general range theorems. We then hint on the relation between the modal non-monotonic logics obtained: we prove that there exist ranges which selectively pick out some of the expansions produced by the many-valued autoepistemic logics introduced in [4, 9], actually the ones with a confidence-bounded set of beliefs. However, an exact characterization of the relation between the various ranges created by the weak many-valued modal axioms still remains to be explored.
Koutras, CD, Nomikos, C & Peppas, P 2002, 'Canonicity and completeness results for many-valued modal logics', Journal of Applied Non-Classical Logics, vol. 12, no. 1, pp. 7-41.View/Download from: Publisher's site
We prove frame determination results for the family of many-valued modal logics introduced by M. Fitting in the early ́90s. Each modal language of this family is based on a Heyting algebra, which serves as the space of truth values, and is interpreted on an interesting version of possible-worlds semantics: the modal frames are directed graphs whose edges are labelled with an element of the underlying Heyting algebra. We introduce interesting generalized forms of the classical axioms D, T, B, 4, and 5 and prove that they are canonical for certain algebraic frame properties, which generalize seriality, reflexivity, symmetry, transitivity and euclideanness. Our results are quite general as they hold for any modal language built on a complete Heyting algebra.
There are two well-developed formalizations of discrete time dynamic systems that evidently share many concerns but suffer from a lack of mutual awareness. One formalization is classical systems and automata theory. The other is the logic of actions in which the situation and event calculi are the strongest representatives. Researchers in artificial intelligence are likely to be familiar with the latter but not the former. This is unfortunate, for systems and automata theory have much to offer by way of insight into problems raised in the logics of action. This paper is an outline of how the input-output view of systems and its associated solution of state realization may be applied to the formalization of dynamics that uses a situation calculus approach. In particular, because the latter usually admits incompletely specified dynamics, which induces a non-deterministic input-output system behavior, we first show that classical state realization can still be achieved if the behavior is causal. This is a novel systems-theoretic result. Then we proceed to indicate how situation calculi dynamic specifications can be understood in systems-theoretic terms, and how automata can be viewed as models of such specifications. As techniques for reasoning about automata are abundant, this will provide yet more tools for reasoning about actions. © 2001 Kluwer Academic Publishers.
A new methodology for developing theories of action has recently emerged which provides means for formally evaluating the correctness of such theories. Yet, for a theory of action to qualify as a solution to the frame problem, not only does it need to produce correct inferences, but moreover, it needs to derive these inferences from a concise representation of the domain at hand. The new methodology however offers no means for assessing conciseness. Such a formal account of conciseness is developed in this paper. Combined with the existing criterion for correctness, our account of conciseness offers a framework where proposed solutions to the frame problem can be formally evaluated. © 2001 Kluwer Academic Publishers.
The Possible Models Approach (PMA) introduced by Winslett, proposes, among other things, a domain-independent criterion for measuring similarity between different states of a dynamic system. The concept of similarity between states (possible worlds) appears also in the area of Belief Revision in the form of a system of spheres. Systems of spheres are in turn connected to epistemic entrenchments by means of the AGM revision functions that the two structures induce. In view of these connections, in this article we study the implications of adopting PMA's criterion of similarity in the context of Belief Revision. More precisely, we formulate conditions that capture PMA's criterion of similarity in terms of systems of spheres (PMA systems of spheres) and we provide an axiomatic characterization of the class of epistemic entrenchments corresponding to systems of spheres that comply with PMA's criterion of similarity (PMA epistemic entrenchments). We also discuss some interesting properties of the class of PMA system of spheres and PMA epistemic entrenchments. Our study is primarily motivated by the role that PMA epistemic entrenchments can play in Reasoning about Action.
Alchourron, Gärdenfors and Makinson have developed and investigated a set of rationality postulates which appear to capture much of what is required of any rational system of theory revision. This set of postulates describes a class of revision functions, however it does not provide a constructive way of defining such a function. There are two principal constructions of revision functions, namely an epistemic entrenchment and a system of spheres. We refer to their approach as the AGM paradigm. We provide a new constructive modeling for a revision function based on a nice preorder on models, and furthermore we give explicit conditions under which a nice preorder on models, an epistemic entrenchment, and a system of spheres yield the same revision function. Moreover, we provide an identity which captures the relationship between revision functions and update operators (as defined by Katsuno and Mendelzon). © 1995, Duke University Press. All Rights Reserved.
Almost three decades ago, DavidMakinson, together with Carlos Alchourron and Peter
G¨ardenfors published their classical work on the logic of theory change, the renowned
'AGM paper' . From this paper the area of Belief Revision was born and hundreds
of future publications drew inspiration from it and contributed to the development of
the field. Yet in this survey we will not focus on what the AGM did do, but rather on
what it left out: iterated belief revision.
Let us set the stage with an example. Vasiliki is an archeologist participating in an
excavation of an ancient temple near Athens. One day her trowel hits on an ancient
Greek vase. The vase is a typical 3rd century BC Greek vase. The design, the painting,
the archeological layer it was discovered in, all confirm without doubt that the vase was
made in Greece some 2300 years ago. The big surprise however came when Vasiliki
looked inside the vase. A small stone tablet with Maya script inscribed on it was lying
inside! The discoverywasmind-blowing. To the young enthusiastic archeologist, eager
to make a name for herself, this was without doubt concrete proof that Columbus was
not the first European to reach America. The ancient Greeks had beat him by 1800
years! History books had to be rewritten! Vasiliki spent the night thinking of all the
changes that had to be made in our theories about ancient Greeks (and perhaps ancient
The theory developed by Alchourron, G¨ardenfors, and Makinson, was designed
to address precisely these kind of scenarios. A rational agent receives new reliable
information ' that (in principle) contradicts her initial belief set K; the agent is thus
forced to move to a new belief set K ˚ ' containing '. Moreover, the new belief set
K ˚ ' has to be a rational change to K given '. The inner workings of the transition
from K to K ˚ ' are studied and formalized in the AGM paper, setting the stage for a
plethora of exciting results to follow over the next three decades.
Gardenfors, P, Williams, M-A, Johnston, B, Billingsley, R, Vitale, J, Peppas, P & Clark, J 2018, 'Event boards as tools for holistic AI', International Workshop on Artificial Intelligence and Cognition 2018, Palermo, Italy.View/Download from: UTS OPUS
Delgrande, J & Peppas, P 2018, 'Incorporating Relevance in Epistemic States in Belief Revision', International Conference on Principles of Knowledge Representation and Reasoning, Tempe, USA.View/Download from: UTS OPUS
Aravanis, T, Demiris, K & Peppas, P 2018, 'Legal reasoning in answer set programming', Proceedings - International Conference on Tools with Artificial Intelligence, ICTAI, International Conference on Tools with Artificial Intelligence, IEEE, Volos, Greece, pp. 302-306.View/Download from: UTS OPUS or Publisher's site
© 2018 IEEE. Answer Set Programming is a declarative problem solving approach, initially tailored to modelling problems in the area of Knowledge Representation and Reasoning. In this article, we provide a knowledge-based system, capable of representing and reasoning about legal knowledge in the context of Answer Set Programming-thus, modelling non-monotonicity that is inherent in legal arguments. The work, although limited to a specific indicative domain, namely, university regulations, has a variety of extensions. The overall approach constitutes a representative implementation of the Answer Set Programming's modelling methodology, as well as an enhancing of the bond between Artificial Intelligence and Legal Science, bringing us a step closer to a successful development of an automated legal reasoning system for real-world applications.
© 2018 Association for Computing Machinery. One of the main shortcomings of the early AGM paradigm is its lack of any guidelines for iterated revision; it formalizes only one-step rational belief revision. Darwiche and Pearl, subsequently, addressed this problem by introducing four additional postulates (the DP postulates), supplementing the AGM ones. Despite the popularity of the DP approach, there are still controversies surrounding the DP postulates. In this article, we prove a conflict between each one of the latter, and one of the most popular and intuitive 'off the shelf' revision functions, that is Dalal's revision operator.
Reis, MDL, Fermé, E & Peppas, P 2017, 'Construction of system of spheres-based transitively relational partial meet multiple contractions: An impossibility result', IJCAI International Joint Conference on Artificial Intelligence, International Joint Conference on Artificial Intelligence, Melbourne, Australia, pp. 5045-5049.View/Download from: UTS OPUS
In this paper we show that, contrary to what is the case in what concerns contractions by a single sentence, there is not a system of spheres-based construction of multiple contractions which generates each and every transitively relational partial meet multiple contraction. Furthermore, we propose two system of spheresbased constructions of multiple contractions which generate (only) transitively relational partial meet multiple contractions.
Aravanis, TI & Peppas, P 2017, 'Belief revision in answer set programming', Proceedings of the 21st Pan-Hellenic Conference on Informatics, Pan-Hellenic Conference on Informatics, ACM, Larissa, Greece, pp. 1-5.View/Download from: UTS OPUS or Publisher's site
© 2017 Association for Computing Machinery. Answer Set Programming is a declarative problem solving approach, initially tailored to modeling problems in the area of Knowledge Representation and Reasoning. In this article,we provide a logic program, in the context of Answer Set Programming framework, that implements the AGM belief revision process, constructed by means of faithful preorders. The above-mentioned approach constitutes a representative implementation of the Answer Set Programming's modeling methodology, as well as a practical method/construction, bringing us a step closer to the successful development of an AGM belief revision system, for real-world applications.
Aravanis, T, Peppas, P & Williams, MA 2017, 'Epistemic-entrenchment characterization of Parikh's axiom', IJCAI International Joint Conference on Artificial Intelligence, International Joint Conference on Artificial Intelligence, International Joint Conferences on Artificial Intelligence Organization, Melbourne, Australia, pp. 772-778.View/Download from: UTS OPUS
In this article, we provide the epistemicentrenchment characterization of the weak version of Parikh's relevance-sensitive axiom for belief revision - known as axiom (P) - for the general case of incomplete theories. Loosely speaking, axiom (P) states that, if a belief set K can be divided into two disjoint compartments, and the new information φ relates only to the first compartment, then the second compartment should not be affected by the revision of K by φ. The above-mentioned characterization, essentially, constitutes additional constraints on epistemicentrenchment preorders, that induce AGM revision functions, satisfying the weak version of Parikh's axiom (P).
Billingsley, R, Billingsley, J, Gärdenfors, P, Peppas, P, Prade, H, Skillicorn, D & Williams, MA 2017, 'The altruistic robot: Do what i want, not just what i say', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), International Conference on Scalable Uncertainty Management, Granada, Spain, pp. 149-162.View/Download from: UTS OPUS or Publisher's site
© Springer International Publishing AG 2017. As autonomous robots expand their application beyond research labs and production lines, they must work in more flexible and less well defined environments. To escape the requirement for exhaustive instruction and stipulated preference ordering, a robot's operation must involve choices between alternative actions, guided by goals. We describe a robot that learns these goals from humans by considering the timeliness and context of instructions and rewards as evidence of the contours and gradients of an unknown human utility function. In turn, this underlies a choice-theory based rational preference relationship. We examine how the timing of requests, and contexts in which they arise, can lead to actions that pre-empt requests using methods we term contemporaneous entropy learning and context sensitive learning. We provide experiments on these two methods to demonstrate their usefulness in guiding a robot's actions.
Peppas, P & Williams, MA 2016, 'Kinetic consistency and relevance in belief revision', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Logics in Artificial Intelligence, European Conference, Springer, Larnaca, Cyprus, pp. 401-414.View/Download from: UTS OPUS or Publisher's site
© Springer International Publishing AG 2016.A critical aspect of rational belief revision that has been neglected by the classical AGM framework is what we call the principle of kinetic consistency. Loosely speaking, this principle dictates that the revision policies employed by a rational agent at different belief sets, are not independent, but ought to be related in a certain way. We formalise kinetic consistency axiomatically and semantically, and we establish a representation result explicitly connecting the two. We then combine the postulates for kinetic consistency, with Parikh's postulate for relevant change, and add them to the classical AGM postulates for revision; we call this augmented set the extended AGM postulates. We prove the consistency and demonstrate the scope of the extended AGM postulates by showing that a whole new class of concrete revision operators introduced hererin, called PD operators, satisfies all extended AGM postulates. PD operators are of interest in their own right as they are natural generalisations of Dalal's revision operator.We conclude the paper with some examples illustrating the strength of the extended AGM postulates, even for iterated revision scenarios.
Karacapilidis, N & Peppas, P 2014, 'On the Formal Assessment of Argumentation Support Systems', SMART DIGITAL FUTURES 2014, KES International Conference on Smart Digital Futures (SDF), IOS Press, Chania, GREECE, pp. 182-189.View/Download from: UTS OPUS or Publisher's site
The development of argumentation support systems for different types of groups and application areas has been receiving growing interest in the last twenty years. Such systems address the needs of a user to interpret and reason about knowledge during a discourse, and demonstrate diverse human and machine reasoning functionalities. However, methodologies to check whether the reasoning mechanisms of such systems adhere to broadly accepted argumentation theories are missing. Provision of such methodologies is of much value, especially in data intensive contexts. The approach described in this paper is a first step towards this direction. Specifically, we formally assess a specific argumentation support system, namely HERMES, against Dungs argumentation theory and prove its correctness as far as the acceptability of arguments is concerned.
Peppas, P & Williams, M 2014, 'Belief Change and Semiorders', http://www.aaai.org/Press/Proceedings/kr14.php, Principles of Knowledge Representation and Reasoning, AAAI, Vienna.View/Download from: UTS OPUS
A central result in the AGM framework for belief revision
is the construction of revision functions in terms
of total preorders on possible worlds. These preorders
encode comparative plausibility: r ă r1 states that the
world r is at least as plausible as r1. Indifference in the
plausibility of two worlds, r, r1, denoted r ' r1, is defined
as r ⊀ r1 and r1 ⊀ r. Herein we take a closer look
at plausibility indifference. We contend that the transitivity
of indifference assumed in the AGM framework
is not always a desirable property for comparative plausibility.
Our argument originates from similar concerns
in preference modelling, where a structure weaker than
a total preorder, called a semiorder, is widely consider
to be a more adequate model of preference. In this paper
we essentially re-construct revision functions using
semiorders instead of total preorders.We formulate postulates
to characterise this new, wider, class of revision
functions, and prove that the postulates are sound and
complete with respect to the semiorder-based construction.
The corresponding class of contraction functions
(via the Levi and Harper Identities) is also characterised
Williams, M & Peppas, P 2014, 'Constructive models for contraction with intransitive plausibility indifference', Logics in Artificial Intelligence - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Logics in Artificial Intelligence, European Conference, Springer Verlag, Madeira, Portugal, pp. 355-367.View/Download from: UTS OPUS or Publisher's site
Plausibility rankings play a central role in modeling Belief Change, and they take different forms depending on the type of belief change under consideration: preorders on possible worlds, epistemic entrenchments, etc. A common feature of all these structures is that plausibility indifference is assumed to be transitive. In a previous article, , we argued that this is not always the case, and we introduced new sets of postulates for revision and contraction (weaker variants of the classical AGM postulates), that are liberated from the indifference transitivity assumption. Herein we complete the task by making the necessary adjustments to the epistemic entrenchment and the partial meet models. In particular we lift the indifference transitivity assumption from both these two models, and we establish representation results connecting the weaker models with the weaker postulates for contraction introduced in .
Delgrande, J, Peppas, P & Woltran, S 2013, 'AGM-style belief revision of logic programs under answer set semantics', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), International Conference on Logic Programming and Non-monotonic Reasoning, Springer, Corunna, Spain, pp. 264-276.View/Download from: UTS OPUS or Publisher's site
In the past few years, several approaches for revision (and update) of logic programs have been studied. None of these however matched the generality and elegance of the original AGM approach to revision in classical logic. One particular obstacle is the underlying nonmonotonicity of the semantics of logic programs. Recently however, specific revision operators based on the monotonic concept of SE-models (which underlies the answer-set semantics of logic programs) have been proposed. Basing revision of logic programs on sets of SE-models has the drawback that arbitrary sets of SE-models may not necessarily be expressed via a logic program. This situation is similar to the emerging topic of revision in fragments of classical logic. In this paper we show how nonetheless classical AGM-style revision can be extended to various classes of logic programs using the concept of SE-models. That is, we rephrase the AGM postulates in terms of logic programs, provide a semantic construction for revision operators, and then in a representation result show that these approaches coincide. This work is interesting because, on the one hand it shows how the AGM approach can be extended to a seemingly nonmonotonic framework, while on the other hand the formal characterization may provide guiding principles for the development of specific revision operators. © 2013 Springer-Verlag.
Delgrande, JP & Peppas, P 2011, 'Revising horn theories', IJCAI International Joint Conference on Artificial Intelligence, International Joint Conference on Artificial Intelligence, AAAI Press, Barcelona, Spain, pp. 839-844.View/Download from: UTS OPUS or Publisher's site
This paper investigates belief revision where the underlying logic is that governing Horn clauses. It proves to be the case that classical (AGM) belief revision doesn't immediately generalise to the Horn case. In particular, a standard construction based on a total preorder over possible worlds may violate the accepted (AGM) postulates. Conversely, Horn revision functions in the obvious extension to the AGM approach are not captured by total preorders over possible worlds. We address these difficulties by first restricting the semantic construction to "well behaved" orderings; and second, by augmenting the revision postulates by an additional postulate. This additional postulate is redundant in the AGM approach but not in the Horn case. In a representation result we show that these two approaches coincide. Arguably this work is interesting for several reasons. It extends AGM revision to inferentially-weaker Horn theories; hence it sheds light on the theoretical underpinnings of belief change, as well as generalising the AGM paradigm. Thus, this work is relevant to revision in areas that employ Horn clauses, such as deductive databases and logic programming, as well as areas in which inference is weaker than classical logic, such as in description logic.
Giannopoulos, V & Peppas, P 2010, 'Associations between constructive models for set contraction', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 113-121.View/Download from: Publisher's site
Belief Change is one of the central research topics in Knowledge Representation and theory revision and contracti on are two of the most important operators in Belief Change. Recently the original axiomatization of revision and contraction was extended to include epistemic input represented by a (possibly infinite) set of sentences (as opposed to a single sentence) giving rise to the operators of set revision (also known as multiple revision) and set contraction. Both set revision and set contraction have been characterized in terms of constructive models called system of spheres and epistemic grasp respectively. Based on these links, in this paper we provide a characterization of set contraction in terms of system of spheres, and we identify the necessary and sufficient conditions under which the system-of-spheres model and the epistemic-grasp model give rise to the same set contraction. © Springer-Verlag Berlin Heidelberg 2010.
Peppas, P, Michael Fotinopoulos, A & Seremetaki, S 2008, 'Conflicts between relevance-sensitive and iterated belief revision', Frontiers in Artificial Intelligence and Applications, pp. 85-88.View/Download from: Publisher's site
© 2008 The authors and IOS Press. All rights reserved. The original AGM paradigm focuses only on one-step belief revision and leaves open the problem of revising a belief state with whole sequences of evidence. Darwiche and Pearl later addressed this problem by introducing extra (intuitive) postulates as a supplement to the AGM ones. A second shortcoming of the AGM paradigm, seemingly unrelated to iterated revision, is that it is too liberal in its treatment of the notion of relevance. Once again this problem was addressed with the introduction of an extra (also very intuitive) postulate by Parikh. The main result of this paper is that Parikh postulate for relevance-sensitive belief revision is inconsistent with each of the Darwiche and Pearl postulates for iterated belief revision.
Foo, N & Peppas, P 2005, 'System properties of action theories', Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science), pp. 416-427.
Logic-based theories of action and automata-based systems theories share concerns about state dynamics that are however not reflected by shared insights. As an example of how to remedy this we examine a simple variety of situation calculus theories from the viewpoint of system-theoretic properties to reveal relationships between them. These provide insights into relationships between logic-based solution policies, and are suggestive of similar relationships for more complex versions. © Springer-Verlag Berlin Heidelberg 2005.
Foo, N & Peppas, P 2005, 'Systems theory: Melding the AI and simulation perspectives', Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science), pp. 14-23.
The discipline of modelling and simulation (MaS) preceded artificial intelligence (AI) chronologically. Moreover, the workers in one area are typically unfamiliar with, and sometimes unsympathetic to, those in the other. One reason for this is that in MaS the formal tools tend to center around analysis and probability theory with statistics, while in AI there is extensive use of discrete mathematics of one form or another, particularly logic. Over the years however, MaS and AI developed many frameworks and perspectives that are more similar than their respective practitioners may care to admit. We will argue in this paper that these parallel developments have led to some myopia that should be over-come because techniques and insights borrowed from the other discipline can be very beneficial. © Springer-Verlag Berlin Heidelberg 2005.
Koutras, CD, Nomikos, C & Peppas, P 2005, 'If I know it then it can't be false (and if it's true then it is not impossible)', International E-Conference on Computer Science 2005, pp. 92-96.
Foo, N, Peppas, P & Zhang, Y 2005, 'Action invariants and system constraints in STRIPS', 7th International Symposium on Logical Formalizations of Commonsense Reasoning, Commonsense 2005.
In [Foo, et.al. 04] we re-visited the problem of converting action specifications into system constraints by re-examining it in the very simple setting of STRIPS, motivated by the simplicity of its simplicity as an action specification language. We showed how to extract action invariants, and then system laws, from STRIPS specifications. This was the consistency part of our method, and we deferred its adequacy to a later report. This paper provides the missing part, thus closing the circle. Here we show that the invariants extracted by our method can be tested by using them to complete partial specifications that may match those which were used as inputs to the extraction phase. Even when the match is incomplete there is interesting ontological information that can be inferred from it. Fixed point theory is used to account for some of the proposed algorithms.
Foo, N, Peppas, P & Zhang, Y 2004, 'Constraints from STRIPS - Preliminary peport', Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science), pp. 670-680.
We re-visit the problem of converting action specifications into system constraints by re-examining it in the very simple setting of STRIPS. This has the merit of making many thorny issues relatively transparent. The paper is in the form of an extended summary of ongoing work and many of the results are merely outlined. But sufficient details are included to indicate where we will be taking things further, and to encourage others to pursue the same objectives. These objectives are in some sense a kind of reverse-engineering, as the database community is evidently familiar with the idea of starting with constraints and then deriving action specifications from them. However in AI reactive systems, action specifications are often the primary entity, so techniques to unearth the implicit constraints can facilitate better designs. © Springer-Verlag Berlin Heidelberg 2004.
Pagnucco, M & Peppas, P 2001, 'Causality and minimal change demystified', IJCAI International Joint Conference on Artificial Intelligence, pp. 125-130.
The Principle of Minimal Change is prevalent in various guises throughout the development of areas such as reasoning about action, belief change and nonmonotonic reasoning. Recent literature has witnessed the proposal of several theories of action that adopt an explicit representation of causality. It is claimed that an explicit notion of causality is able to deal with the frame problem in a manner not possible with traditional approaches based on minimal change. However, such claims remain untested by all but representative examples. It is our purpose here to objectively test these claims in an abstract sense; to determine whether an explicit representation of causality is capable of providing something that the Principle of Minimal Change is unable to capture. Working towards this end, we provide a precise characterisation of the limit of applicability of minimal change.
Prokopenko, M, Pagnucco, M, Peppas, P & Nayak, A 2000, 'A unifying semantics for causal ramifications', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 38-49.
A unifying semantic framework for different reasoning approaches provides an ideal tool to compare these competing alternatives. However, it has been shown recently that a pure preferential semantics alone is not capable of providing such a unifying framework. On the other hand, variants of preferential semantics augmented by additional structures on the state space have been successfully used to characterise some influential approaches to reasoning about action and causality. The primary aim of this paper is to provide an augmented preferential semantics that is general enough to unify two prominent frameworks for reasoning about action and causality - Sandewall's causal propagation semantics  and Thielscher's causal relationships approach . There are indications that these and other different augmented preferential semantical approaches can by unified into a general framework, and provide the unified semantics that is lacking so far. © Springer-Verlag Berlin Heidelberg 2000.
Prokopenko, M, Pagnucco, M, Peppas, P & Nayak, A 1999, 'Causal propagation semantics—a study', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 378-392.View/Download from: Publisher's site
© Springer-Verlag Berlin Heidelberg 1999. A unifying semantic framework for different reasoning approaches provides an ideal tool to compare these competing alternatives. A historic example is Kripke's possible world semantics that provided a unifying framework for different systems of modal logic. More recently, Shoham's work on preferential semantics similarly provided a much needed framework to uniformly represent and compare a variety of nonmonotonic logics (including some logics of action). The present work develops a novel type of semantics for a particuleir causal approach to reasoning about action. The basic idea is to abandon the standard statespace of possible worlds and consider instead a larger set of possibiUties—a hyper-space—tracing the effects of auctions (including indirect effects) with the states in the hyper-space. Intuitively, the purpose of these hyper-states is to supply extra context to record the process of causality.
Peppas, P, Pagnucco, M, Prokopenko, M, Foo, NY & Nayak, A 1999, 'Preferential semantics for causal systems', IJCAI International Joint Conference on Artificial Intelligence, pp. 118-123.
In the present work we examine the causal theory of actions put forward by McCain and Turner [McCain and Turner, 1995] for determining ramifications. Our principal aim is to provide a characterisation of this causal theory of actions in terms of a Shoham-like preferential semantics [Shoham, 19881. This would have a twofold advantage: it would place McCain and Turner's theory in perspective, allowing a comparison with other logics of action; and, it would allow us to glean further insights into the nature of causality underlying their work. We begin by showing that our aim is not attainable by a preferential mechanism alone. At this point we do not abandon preferential semantics altogether but augment it in order to arrive at the desired result. We draw f he following moral which is at the heart of our paper: two components - minimal change under a preferential structure and causality - are required to provide a concise solution to the frame and ramification problems.
Prokopenko, M & Peppas, P 1998, 'Modelling inertia in action languages', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 234-247.View/Download from: Publisher's site
© Springer-Verlag Berlin Heidelberg 1998. Logic-based approaches to reasoning about actions, change and causality, highlight efficient representation and processing of domain background knowledge as an important task. Action theories recently developed in the framework of action languages with inertia and ramifications [20,14] not only adopt the principle of minimal change reinforced with the policy of categorisation (assigning different degrees of inertia to language elements) but also try to incorporate background causal knowledge. In this paper we aim to trace the evolution of action languages and to explore interactions between ontological characteristics of action domains such as inertia and causality. Such an analysis should clarify how possible solutions to the frame and the ramification problems are affected by applying the policy of categorisation to causal' domains. We first attempt to identify conditions (more precisely, restrictions) which preserve the meaning of domain descriptions when moving among various analysed languages. Relaxing such restrictions can help in evaluating the role of the frame concept (and policy of categorisation, in general) in an action language with fluent-triggered causality.
Peppas, P, Pagnucco, M, Prokopenko, M & Foo, N 1997, 'Preferential semantics for causal fixpoints', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 197-206.
© Springer-Verlag Berlin Heidelberg 1997.In this paper we concentrate on the causal theory of action developed by McCain and Turner  for computing ramifications. Our aim here is to characterise this theory of action in terms of a preferentialstyle semantics in the spirit of Shoham . Such a result would not only place McCain and Turner's theory in a uniform setting, facilitating comparison with other logics of action, but also give a clearer insight into the nature and behaviour of causality captured by their framework. We first show that this objective is not attainable via a traditional preferential semantics. However, preferential semantics is not abandoned entirely. Rather, it is augmented to arrive at the desired result. We maintain that two components — minimal change and causality — are essential in providing a (concise) solution to the frame and ramification problems.
Foo, N, Peppas, P & Zhang, Y 1997, 'Inductive properties of states', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 227-235.
© Springer-Verlag Berlin Heidelberg 1997.In the situation calculus states are often distinguished from situations by the assumption that situations are paths in a rooted tree while a state is a particular truth assignment to the fluents. It is then possible that two situations have end points that agree on all fluents, i.e., are the same state, and yet be distinct from the perspective of situations. This has the merit of making inductive proofs simple as it introduces two axioms amounting to enforcing the rooted tree structure that are used as trivial bases for the inductions. In this paper we show that the tree structure is dispensable for induction when the underlying system is deterministic, thus elevating the state perspective to equal status.
Foo, NY, Nayak, A, Pagnucco, M, Peppas, P & Zhang, Y 1997, 'Action localness, genericity and invariants in STRIPS', IJCAI-97 - PROCEEDINGS OF THE FIFTEENTH INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE, VOLS 1 AND 2, pp. 549-554.
Peppas, P, Pagnucco, M, Prokopenko, M & Foo, N 1997, 'Preferential semantics for causal fixpoints', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 197-206.
© Springer-Verlag Berlin Heidelberg 1997. In this paper we concentrate on the causal theory of action developed by McCain and Turner  for computing ramifications. Our aim here is to characterise this theory of action in terms of a preferentialstyle semantics in the spirit of Shoham . Such a result would not only place McCain and Turner's theory in a uniform setting, facilitating comparison with other logics of action, but also give a clearer insight into the nature and behaviour of causality captured by their framework. We first show that this objective is not attainable via a traditional preferential semantics. However, preferential semantics is not abandoned entirely. Rather, it is augmented to arrive at the desired result. We maintain that two components — minimal change and causality — are essential in providing a (concise) solution to the frame and ramification problems.
Foo, N, Peppas, P & Zhang, Y 1997, 'Inductive properties of states', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 227-235.
© Springer-Verlag Berlin Heidelberg 1997. In the situation calculus states are often distinguished from situations by the assumption that situations are paths in a rooted tree while a state is a particular truth assignment to the fluents. It is then possible that two situations have end points that agree on all fluents, i.e., are the same state, and yet be distinct from the perspective of situations. This has the merit of making inductive proofs simple as it introduces two axioms amounting to enforcing the rooted tree structure that are used as trivial bases for the inductions. In this paper we show that the tree structure is dispensable for induction when the underlying system is deterministic, thus elevating the state perspective to equal status.
PEPPAS, P & WOBCKE, W 1992, 'ON THE USE OF EPISTEMIC ENTRENCHMENT IN REASONING ABOUT ACTION', ECAI 92 - 10TH EUROPEAN CONFERENCE ON ARTIFICIAL INTELLIGENCE : PROCEEDINGS, pp. 403-407.