The Experts below are selected from a list of 327 Experts worldwide ranked by ideXlab platform
Alexander Bochman - One of the best experts on this subject based on the ideXlab platform.
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A foundational theory of belief and belief change
Artificial Intelligence, 1999Co-Authors: Alexander BochmanAbstract:Abstract We suggest a foundational representation for the notion of belief and belief change process based on the notion of an epistemic state and its associated Scott Consequence Relation. We study the basic belief change operations in this framework and compare the resulting theory with related approaches.
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on the Relation between default and modal nonmonotonic reasoning
Artificial Intelligence, 1998Co-Authors: Alexander BochmanAbstract:The notion of a default Consequence Relation is introduced as a generalization of both default and modal formalizations of nonmonotonic reasoning. It is used to study a general problem of correspondence between these two formalisms.
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KR - On the Relation Between Default and Modal Consequence Relations
Principles of Knowledge Representation and Reasoning, 1994Co-Authors: Alexander BochmanAbstract:The notion of a default Consequence Relation is introduced as a generalization of both default and modal formalizations of nonmonotonic reasoning. It is used to study a general problem of correspondence between these two formalisms. As is shown, in many cases each of them can be translated into the other.
Andrzej Pietruszczak - One of the best experts on this subject based on the ideXlab platform.
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A Method of Generating Modal Logics Defining Jaśkowski’s Discussive D2 Consequence
Logic Argumentation & Reasoning, 2014Co-Authors: Marek Nasieniewski, Andrzej PietruszczakAbstract:Jaśkowski’s logic D 2 is usually understood as a set of discussive formulae. Studying Jaśkowski’s paper one can also find a Consequence Relation (the D 2 -Consequence). The logic D 2 was meant to express this Consequence Relation. Since the logic D 2 was formulated with the help of a modal logic, the Consequence Relation is also defined in the modal language. It is known that the logic D 2 can be defined by other modal logics than S5. A similar question arises as regards the Consequence Relation. In Nasieniewski and Pietruszczak (On modal logics defining Jaśkowski’s D2-Consequence. In: Tanaka K, Berto F, Mares E, Paoli F (eds) Paraconsistency: logic and applications. Logic, epistemology and the unity of science, chap 8, vol 26. Springer, Dordrecht/New York, pp 141–161, 2013) there are given modal logics other than S5 which define exactly the same Consequence Relation. In the present paper we try to develop a more general method of defining modal logics which also allow to define the D 2 -Consequence.
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The axiomatization of Horst Wessel’s strict logical Consequence Relation
Logic and Logical Philosophy, 2004Co-Authors: Andrzej PietruszczakAbstract:In his book from 1984 Horst Wessel presents the system of strict logical Consequence Fs (see also (Wessel, 1979)). The author maintained that this system axiomatized the Relation |=s of strict logical Consequence between formulas of Classical Propositional Calculi (CPC). Let |= be the classical Consequence Relation in CPC. The Relation |=s is defined as follows: \phi |=s \psi iff \phi |= \psi, every variable from \psi occurs in \phi and neither \phi is a contradiction nor \psi is a tautology. Clearly, if \phi |=s \psi, then neither \phi is a tautology nor \psi is a contradiction. Intuitions connected with the Relation |=s were presented in (Wessel, 1984). The analysis of the Relation |=s is also carried out in (Pietruszczak, 2004). In the present paper we will show that the system Fs is not a complete axiomatization of the Relation |=s. Moreover, we will present the system VF s that is an «extension to completeness» of the Fs.
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the axiomatization of horst wessel s strict logical Consequence Relation
Logic and Logical Philosophy, 2004Co-Authors: Andrzej PietruszczakAbstract:In his book from 1984 Horst Wessel presents the system of strict logical Consequence Fs (see also (Wessel, 1979)). The author maintained that this system axiomatized the Relation |=s of strict logical Consequence between formulas of Classical Propositional Calculi (CPC). Let |= be the classical Consequence Relation in CPC. The Relation |=s is defined as follows: \phi |=s \psi iff \phi |= \psi, every variable from \psi occurs in \phi and neither \phi is a contradiction nor \psi is a tautology. Clearly, if \phi |=s \psi, then neither \phi is a tautology nor \psi is a contradiction. Intuitions connected with the Relation |=s were presented in (Wessel, 1984). The analysis of the Relation |=s is also carried out in (Pietruszczak, 2004). In the present paper we will show that the system Fs is not a complete axiomatization of the Relation |=s. Moreover, we will present the system VF s that is an «extension to completeness» of the Fs.
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The Consequence Relation preserving logical information
Logic and Logical Philosophy, 2004Co-Authors: Andrzej PietruszczakAbstract:Information is contained in statements and «flows» from their structure and meaning of expressions they contain. The information that flows only from the meaning of logical constants and logical structure of statements we will call logical information. In this paper we present a formal explication of this notion which is proper for sentences being Boolean combination of atomic sentences. 1 Therefore we limit ourselves to analyzing logical information flowing only from the meaning of truth-value connectives and logical structure of sentences connected with these connectives.
Ka-shu Wong - One of the best experts on this subject based on the ideXlab platform.
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Sound and complete inference rules for SE-Consequence
Journal of Artificial Intelligence Research, 2008Co-Authors: Ka-shu WongAbstract:The notion of strong equivalence on logic programs with answer set semantics gives rise to a Consequence Relation on logic program rules, called SE-Consequence. We present a sound and complete set of inference rules for SE-Consequence on disjunctive logic programs.
Gunther Gediga - One of the best experts on this subject based on the ideXlab platform.
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a note on the correspondence among entail Relations rough set dependencies and logical Consequence
Journal of Mathematical Psychology, 2001Co-Authors: Ivo Duntsch, Gunther GedigaAbstract:Abstract In this note, we report that entail Relations defined in the context of knowledge spaces are equivalent to the dependence Relations of rough set data analysis and Tarski's Consequence Relation of monotone logic. We also discuss the connection between these and related structures.
Philip Kremer - One of the best experts on this subject based on the ideXlab platform.
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SUPERVALUATION FIXED-POINT LOGICS OF TRUTH
Journal of Philosophical Logic, 2008Co-Authors: Philip Kremer, Alasdair UrquhartAbstract:Michael Kremer defines fixed-point logics of truth based on Saul Kripke’s fixed point semantics for languages expressing their own truth concepts. Kremer axiomatizes the strong Kleene fixed-point logic of truth and the weak Kleene fixed-point logic of truth, but leaves the axiomatizability question open for the supervaluation fixed-point logic of truth and its variants. We show that the principal supervaluation fixed point logic of truth, when thought of as Consequence Relation, is highly complex: it is not even analytic. We also consider variants, engendered by a stronger notion of ‘fixed point’, and by variant supervaluation schemes. A ‘logic’ is often thought of, not as a Consequence Relation, but as a set of sentences – the sentences true on each interpretation. We axiomatize the supervaluation fixed-point logics so conceived.
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Some Supervaluation-based Consequence Relations
Journal of Philosophical Logic, 2003Co-Authors: Philip Kremer, Michael KremerAbstract:In this paper, we define some Consequence Relations based on supervaluation semantics for partial models, and we investigate their properties. For our main Consequence Relation, we show that natural versions of the following fail: upwards and downwards Lowenheim–Skolem, axiomatizability, and compactness. We also consider an alternate version for supervaluation semantics, and show both axiomatizability and compactness for the resulting Consequence Relation.