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1
Content available remote A Dynamic Logic Account of Active Integrity Constraints
Feuillade Guillaume, Herzig Andreas, Rantsoudis Christos
Fundamenta Informaticae
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2019
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Vol. 169, nr 3
179--210
EN
Active integrity constraints have been introduced in the database community as a way to restore integrity based on a set of preferred update actions. We view active integrity constraints as dynamic logic programs and show how several semantics of database repair that were proposed in the literature can be characterised in Dynamic Logic of Propositional Assignments DL-PA. We moreover propose a new definition of repair which makes use of the programs of Dynamic Logic to provide repair solutions based on an iterating procedure. After an analysis of their properties and a comparison to the previous approaches, we provide complexity results for the problem of existence of these new repairs. Furthermore, an extension on databases with history is explored and the behavior of the various repairs is adjusted to work in this setting. For all these definitions we provide DL-PA counterparts of reasoning and decision problems, such as the existence of a repair or the existence of a unique repair.
2
Content available Static and dynamic vector semantics for lambda calculus models of natural language
Sadrzadeh M., Muskens R.
Journal of Language Modelling
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2018
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Vol. 6, No. 2
319--351
EN
Vector models of language are based on contextual aspects of language – distributions of words and how they co-occur in text. Truth conditional models focus on logical aspects of language and on how words combine to contribute to these aspects. In the truth conditional approach, there is a focus on the denotations of phrases. In vector models, the degree of co-occurrence of words in context determines how similar their meanings are. The two approaches have complementary virtues. In this paper we combine them and develop a vector semantics for language, based on the typed lambda calculus. We provide two types of vector semantics: a static one using techniques from the truth conditional tradition, and a dynamic one with a form of interpretation inspired by Heim’s context change potentials. We show, with examples, how the dynamic model can be applied to entailment between a corpus and a sentence.
3
Content available remote A Dynamic-Logical Characterization of Solutions to Sight-limited Extensive Games
Liu C., Liu F., Su K.
Fundamenta Informaticae
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2018
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Vol. 158, nr 1/3
149--169
EN
An unrealistic assumption in classical extensive game theory is that the complete game tree is fully perceivable by all players. To weaken this assumption, a class of games (called games with short sight) was proposed in literature, modelling the game scenarios where players have only limited foresight of the game tree due to bounded resources and limited computational ability. As a consequence, the notions of equilibria in classical game theory were refined to fit games with short sight. A crucial issue that thus arises is to determine whether a strategy profile is a solution to a game. To study this issue and address the underlying idea and theory on players’ decisions in such games, we adopt a logical way. Specifically, we develop a logic called DLS through which features of these games are demonstrated. More importantly, it enables us to characterize the solutions to these games via formulas of this logic. Moreover, we study the algorithm for model checking DLS, which is shown to be PTIME-complete in the size of the model. This work not only provides an insight into a more realistic model in game theory, but also enriches the possible applications of logic.
4
Content available remote Modal Probability, Belief, and Actions
Herzig A.
Fundamenta Informaticae
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2003
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Vol. 57, nr 2-4
323--344
EN
We investigate a modal logic of probability with a unary modal operator expressing that a proposition is more probable than its negation. Such an operator is not closed under conjunction, and its modal logic is therefore non-normal. Within this framework we study the relation of probability with other modal concepts: belief and action. We focus on the evolution of belief, and propose an integration of revision. For that framework we give a regression algorithm.
5
Content available remote Evolution of Collective Commitment during Teamwork
Dunin-Kęplicz B., Verbrugge R.
Fundamenta Informaticae
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2003
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Vol. 56, nr 4
329-371
EN
In this paper we aim to describe dynamic aspects of social and collective attitudes in teams of agents involved in Cooperative Problem Solving (CPS). Particular attention is given to the strongest motivational attitude, collective commitment, and its evolution during team action. First, building on our previous work, a logical framework is sketched in which a number of relevant social and collective attitudes is formalized, leading to the plan-based definition of collective commitments. Moreover, a dynamic logic component is added to this framework in order to capture the effects of the complex actions that are involved in the consecutive stages of CPS, namely potential recognition, team formation, plan formation and team action. During team action, the collective commitment leads to the execution of agent-specific actions. A dynamic and unpredictable environment may, however, cause the failure of some of these actions, or present the agents with new opportunities. The abstract reconfiguration algorithm, presented in a previous paper, is designed to handle the re-planning needed in such situations in an efficient way. In this paper, the dynamic logic component of the logical framework addresses issues pertaining to adjustments in collective commitment during the reconfiguration process.
6
Content available remote A Modal Characterization of Nash Equilibrium
Harrenstein P., Van der Hoek W., Meyer J.-J., Witteveen C.
Fundamenta Informaticae
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2003
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Vol. 57, nr 2-4
281--321
EN
Multi-agent systems comprise entities whose individual decision making behavior may depend on one another's. Game-theory provides apposite concepts to reason in a mathematically precise fashion about such interactive and interdependent situations. This paper concerns a logical analysis of the game-theoretical notions of Nash equilibrium and its subgame perfect variety as they apply to a particular class of extensive games of perfect information. Extensive games are defined as a special type of labelled graph and we argue that modal languages can be employed in their description. We propose a logic for a multi-modal language and prove its completeness with respect to a class of frames that correspond with a particular class of extensive games. In this multi-modal language (subgame perfect) Nash equilibria can be characterized. Finally, we show how this approach can formally be refined by using Propositional Dynamic Logic ( PDL), though we leave completeness as an open question.
7
Content available remote A fragment of Intuitionistic Dynamic Logic
Celani S.A.
Fundamenta Informaticae
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2001
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Vol. 46, nr 3
187-197
EN
We present a fragment of Propositional Dynamic Logic based on the Intuitionistic Propositional Logic. We show that this logic has the finite model property, and therefore, is frame-complete
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