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8Algorithms in cognition, informatics and logic: A position manifestoLogic Journal of the IGPL 18 (6): 763-768. 2010.
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10Adding a temporal dimension to a logic systemJournal of Logic, Language and Information 1 (3): 203-233. 1992.We introduce a methodology whereby an arbitrary logic system L can be enriched with temporal features to create a new system T(L). The new system is constructed by combining L with a pure propositional temporal logic T (such as linear temporal logic with “Since” and “Until”) in a special way. We refer to this method as “adding a temporal dimension to L” or just “temporalising L”. We show that the logic system T(L) preserves several properties of the original temporal logic like soundness, comple…Read more
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32Cumulativity without closure of the domain under finite unionsReview of Symbolic Logic 1 (3): 372-392. 2008.For nonmonotonic logics, Cumulativity is an important logical rule. We show here that Cumulativity fans out into an infinity of different conditions, if the domain is not closed under finite unions
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Proof theory for fuzzy logics. Applied Logic Series, vol. 36Bulletin of Symbolic Logic 16 (3): 415-419. 2010.
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20Investigations in Modal and Tense Logics with Application to Problems in Philosophy and LinguisticsJournal of Symbolic Logic 44 (4): 656-657. 1979.
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35On modal logics characterized by models with relative accessibility relations: Part IIStudia Logica 66 (3): 349-384. 2000.This work is divided in two papers (Part I and Part II). In Part I, we introduced the class of Rare-logics for which the set of terms indexing the modal operators are hierarchized in two levels: the set of Boolean terms and the set of terms built upon the set of Boolean terms. By investigating different algebraic properties satisfied by the models of the Rare-logics, reductions for decidability were established by faithfully translating the Rare-logics into more standard modal logics (some of th…Read more
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36Semantical Investigations in Heyting's Intuitionistic LogicJournal of Symbolic Logic 51 (3): 824-824. 1986.
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42A theory of hierarchical consequence and conditionalsJournal of Logic, Language and Information 19 (1): 3-32. 2010.We introduce -ranked preferential structures and combine them with an accessibility relation. -ranked preferential structures are intermediate between simple preferential structures and ranked structures. The additional accessibility relation allows us to consider only parts of the overall -ranked structure. This framework allows us to formalize contrary to duty obligations, and other pictures where we have a hierarchy of situations, and maybe not all are accessible to all possible worlds. Repre…Read more
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An intuitionistic basis for non-monotonic reasoningIn Philippe Smets (ed.), Non-standard logics for automated reasoning, Academic Press. 1988.
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13Review: Saul A. Kripke, Semantical Considerations for Modal Logics (review)Journal of Symbolic Logic 34 (3): 501-501. 1969.
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20Voting by Eliminating QuantifiersStudia Logica 92 (3): 365-379. 2009.Mathematical theory of voting and social choice has attracted much attention. In the general setting one can view social choice as a method of aggregating individual, often conflicting preferences and making a choice that is the best compromise. How preferences are expressed and what is the “best compromise” varies and heavily depends on a particular situation. The method we propose in this paper depends on expressing individual preferences of voters and specifying properties of the resulting ra…Read more
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3Frontiers of combining systems 2 (edited book)Research Studies Press. 2000.The International workshop 'Frontiers of Combining Systems' is the only forum that is exclusively devoted to research efforts in this interdisciplinary area. This volume contains selected, edited papers from the second installment of the workshop. The contributions range from theorem proving, rewriting and logic to systems and constraints. While there is a clear emphasis on automated tools and logics, the contributions to this volume show that there exists a rapidly expanding body of solutions o…Read more
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99Sequential Dynamic LogicJournal of Logic, Language and Information 21 (3): 279-298. 2012.We introduce a substructural propositional calculus of Sequential Dynamic Logic that subsumes a propositional part of dynamic predicate logic, and is shown to be expressively equivalent to propositional dynamic logic. Completeness of the calculus with respect to the intended relational semantics is established.
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18Products of modal logics and tensor products of modal algebrasJournal of Applied Logic 12 (4): 570-583. 2014.
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24A normal logic that is complete for neighborhood frames but not for Kripke framesTheoria 40 (3): 148-153. 1974.
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3This volume constitutes the proceedings of the First International Conference on Temporal Logic (ICTL '94), held at Bonn, Germany in July 1994. Since its conception as a discipline thirty years ago, temporal logic is studied by many researchers of numerous backgrounds; presently it is in a stage of accelerated dynamic growth. This book, as the proceedings of the first international conference particularly dedicated to temporal logic, gives a thorough state-of-the-art report on all aspects of tem…Read more
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40Montague Type Semantics for Modal Logics with Propositional QuantifiersMathematical Logic Quarterly 17 (1): 245-249. 1971.
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70A general theory of structured consequence relationsTheoria 10 (2): 49-78. 1995.There are several areas in logic where the monotonicity of the consequence relation fails to hold. Roughly these are the traditional non-monotonic systems arising in Artificial Intelligence (such as defeasible logics, circumscription, defaults, ete), numerical non-monotonic systems (probabilistic systems, fuzzy logics, belief functions), resource logics (also called substructural logics such as relevance logic, linear logic, Lambek calculus), and the logic of theory change (also called belief re…Read more
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8Do we really need tenses other than future and past?In Rainer Bäuerle, Urs Egli & Arnim von Stechow (eds.), Semantics from different points of view, Springer Verlag. pp. 15--20. 1979.
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12Handbook of Philosophical Logic, Volume II. Extensions of Classical LogicPhilosophical Quarterly 36 (142): 101. 1986.
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54Logical Modes of Attack in Argumentation NetworksStudia Logica 93 (2): 199-230. 2009.This paper studies methodologically robust options for giving logical contents to nodes in abstract argumentation networks. It defines a variety of notions of attack in terms of the logical contents of the nodes in a network. General properties of logics are refined both in the object level and in the metalevel to suit the needs of the application. The network-based system improves upon some of the attempts in the literature to define attacks in terms of defeasible proofs, the so-called rule-bas…Read more
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110Adding a temporal dimension to a logic systemJournal of Logic, Language and Information 1 (3): 203-233. 1992.We introduce a methodology whereby an arbitrary logic system L can be enriched with temporal features to create a new system T(L). The new system is constructed by combining L with a pure propositional temporal logic T (such as linear temporal logic with Since and Until) in a special way. We refer to this method as adding a temporal dimension to L or just temporalising L. We show that the logic system T(L) preserves several properties of the original temporal logic like soundness, completeness, …Read more
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31Second-Order Quantifier Elimination in Higher-Order Contexts with Applications to the Semantical Analysis of ConditionalsStudia Logica 87 (1): 37-50. 2007.Second-order quantifier elimination in the context of classical logic emerged as a powerful technique in many applications, including the correspondence theory, relational databases, deductive and knowledge databases, knowledge representation, commonsense reasoning and approximate reasoning. In the current paper we first generalize the result of Nonnengart and Szałas [17] by allowing second-order variables to appear within higher-order contexts. Then we focus on a semantical analysis of conditio…Read more