A Simple Separation Logic

International audienceThe kinds of models that are usually considered in separation logic are structures such as words, trees, and more generally pointer structures (heaps). In this paper we introduce the separation logic of much simpler structures, viz. sets. The models of our set separation logic are nothing but valuations of classical propositional logic. Separating a valuation V consists in splitting it up into two partial valuations v 1 and v 2. Truth of a formula φ 1 * φ 2 in a valuation V can then be defined in two different ways: first, as truth of φ 1 in all total extensions of v 1 and truth of φ 2 in all total extensions of v 2; and second, as truth of φ 1 in some total extension of v 1 and truth of φ 2 in some total extension of v 2. The first is an operator of separation of resources: the update of φ 1 * φ 2 by ψ is the conjunction of the update of φ 1 by ψ and the update of φ 2 by ψ; in other words, φ 1 * φ 2 can be updated independently. The second is an operator of separation of processes: updates by ψ 1 * ψ 2 can be performed independently. We show that the satisfiability problem of our logic is decidable in polynomial space (PSPACE). We do so by embedding it into dynamic logic of propositional assignments (which is PSPACE complete). We moreover investigate its applicability to belief update and belief revision, where the separation operators allow to formulate natural requirements on independent pieces of information

De DEL à EDL ou comment illustrer la puissance des événements inverses

La logique épistémique dynamique (DEL) introduite par Baltag et col. et la logique propositionnelle dynamique (PDL) proposent différentes sémantiques aux événements. La seconde se prête facilement à l'introduction d'événements inverses et de relations d'accessibilité épistémiques. Nous appelons EDL le formalisme résultant. Nous montrons alors que DEL peut être traduit dans EDL grâce à cet emploi d'événements inverses. Il s'ensuit que EDL est plus expressive et générale que DEL . Dynamic epistemic logic (DEL) as viewed by Baltag et col. and propositional dynamic logic (PDL) offer different semantics of events. It turns out that converse events and epistemic accessibility relations can be easily introduced in PDL . We call EDL the resulting formalism. We then show that DEL can be translated into EDL thanks to this use of converse events. It follows that EDL is more expressive and general than DEL

Exploring the power of converse events

Dynamic epistemic logic as viewed by Baltag, Moss and Solecki (DEL) and propositional dynamic logic (PDL) offer different semantics of events. On the one hand, DEL adds dynamics to epistemic logic by introducing so-called event models as syntactic objects into the language. On the other hand, PDL has instead transition relations between possible worlds. This last approach allows to easily introduce converse events. In this paper we add epistemics to this, and call the resulting logic epistemic dynamic logic (EDL). We show that DEL can be translated into EDL thanks to this use of the converse operator: it enables us to translate the structure of the event model directly within a particular axiomatization of EDL, without having to refer to a particular epistemic event model in the language (as done in DEL). It follows that EDL is more expressive and general than DEL and we characterize semantically and syntactically in EDL this embedding of DEL

An Ordinal View of Independence with Application to Plausible Reasoning

An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability theory, and the two others are based on the notion of conditional possibility. These two have enough expressive power to support the whole possibility theory, and a complete axiomatization is provided for the strongest one. Moreover we show that weak independence is well-suited to the problems of belief change and plausible reasoning, especially to address the problem of blocking of property inheritance in exception-tolerant taxonomic reasoning.Comment: Appears in Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI1994

Trust-based personal information management in SOA

International audienceService Oriented Architecture (SOA) enables cooperation in an open and highly concurrent context. In this paper, we investigate the management of personal information by an SOA service consumer while invoking composed services, where we will study the balance between quality of service (that works better when provided with our personal data) and the consumer’s data access policy.We present a service architecture that is based on an open epistemic multi-agent. We describe a logic-based trust module that a service consumer can use to assess and explain his trust toward composed services (which are perceived as composed actions executed by a group of agents in the system).We then illustrate our solution in a case study involving a professional social network

A Simple Separation Logic

The kinds of models that are usually considered in separation logic are structures such as words, trees, and more generally pointer structures (heaps). In this paper we introduce the separation logic of much simpler structures, viz. sets. The models of our set separation logic are nothing but valuations of classical propositional logic. Separating a valuation V consists in splitting it up into two partial valuations v 1 and v 2. Truth of a formula φ 1 * φ 2 in a valuation V can then be defined in two different ways: first, as truth of φ 1 in all total extensions of v 1 and truth of φ 2 in all total extensions of v 2; and second, as truth of φ 1 in some total extension of v 1 and truth of φ 2 in some total extension of v 2. The first is an operator of separation of resources: the update of φ 1 * φ 2 by ψ is the conjunction of the update of φ 1 by ψ and the update of φ 2 by ψ; in other words, φ 1 * φ 2 can be updated independently. The second is an operator of separation of processes: updates by ψ 1 * ψ 2 can be performed independently. We show that the satisfiability problem of our logic is decidable in polynomial space (PSPACE). We do so by embedding it into dynamic logic of propositional assignments (which is PSPACE complete). We moreover investigate its applicability to belief update and belief revision, where the separation operators allow to formulate natural requirements on independent pieces of information

Logics for multi-agent systems: a critical overview

International audienceFormal models for multi-agent systems (MAS) have been introduced and studied in various areas, not only in distributed systems and AI, but also in economics and the social sciences. I will focus on logical models of the central concepts of knowledge, belief, time, and action, and will give an overview of the existing logics for MAS from a knowledge representation point of view. I will classify various MAS logics according to the epistemic and the action dimension, distinguishing individual and group action and individual and group knowledge. I will highlight problematic aspects of each of the standard accounts, including frame axioms, strategy contexts and uniform strategies

Belief merging in Dynamic Logic of Propositional Assignments

International audienceWe study syntactical merging operations that are defined semantically by means of the Hamming distance between valuations; more precisely, we investigate the Σ-semantics, Gmax-semantics and max-semantics. We work with a logical language containing merging operators as connectives, as opposed to the metalanguage operations of the literature. We capture these merging operators as programs of Dynamic Logic of Propositional Assignments DL-PA. This provides a syntactical characterisation of the three semantically defined merging operators, and a proof system for DL-PA therefore also provides a proof system for these merging operators. We explain how PSPACE membership of the model checking and satisfiability problem of star-free DL-PA can be extended to the variant of DL-PA where symbolic disjunctions that are parametrised by sets (that are not defined as abbreviations, but are proper connectives) are built into the language. As our merging operators can be polynomially embedded into this variant of DL-PA, we obtain that both the model checking and the satisfiability problem of a formula containing possibly nested merging operators is in PSPACE