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17
Cutfree Display Calculi for Nominal Tense Logics
 Conference on Tableaux Calculi and Related Methods (TABLEAUX
, 1998
"... . We define cutfree display calculi for nominal tense logics extending the minimal nominal tense logic (MNTL) by addition of primitive axioms. To do so, we use a translation of MNTL into the minimal tense logic of inequality (MTL 6= ) which is known to be properly displayable by application of Krac ..."
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Cited by 16 (7 self)
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. We define cutfree display calculi for nominal tense logics extending the minimal nominal tense logic (MNTL) by addition of primitive axioms. To do so, we use a translation of MNTL into the minimal tense logic of inequality (MTL 6= ) which is known to be properly displayable by application of Kracht's results. The rules of the display calculus ffiMNTL for MNTL mimic those of the display calculus ffiMTL 6= for MTL 6= . Since ffiMNTL does not satisfy Belnap's condition (C8), we extend Wansing's strong normalisation theorem to get a similar theorem for any extension of ffiMNTL by addition of structural rules satisfying Belnap's conditions (C2)(C7). Finally, we show a weak Sahlqviststyle theorem for extensions of MNTL, and by Kracht's techniques, deduce that these Sahlqvist extensions of ffiMNTL also admit cutfree display calculi. 1 Introduction Background: The addition of names (also called nominals) to modal logics has been investigated recently with different motivations; see...
On the complexity of fragments of modal logics
 Advances in Modal Logic  Volume 5
, 2005
"... abstract. We study and give a summary of the complexity of 15 basic normal monomodal logics under the restriction to the Horn fragment and/or bounded modal depth. As new results, we show that: a) the satisfiability problem of sets of Horn modal clauses with modal depth bounded by k ≥ 2 in the modal ..."
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Cited by 9 (2 self)
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abstract. We study and give a summary of the complexity of 15 basic normal monomodal logics under the restriction to the Horn fragment and/or bounded modal depth. As new results, we show that: a) the satisfiability problem of sets of Horn modal clauses with modal depth bounded by k ≥ 2 in the modal logics K 4 and KD4 is PSPACEcomplete, in K is NPcomplete; b) the satisfiability problem of modal formulas with modal depth bounded by 1 in K 4, KD4, and S4 is NPcomplete; c) the satisfiability problem of sets of Horn modal clauses with modal depth bounded by 1 in K, K 4, KD4, and S4 is PTIMEcomplete. In this work, we also study the complexity of the multimodal logics Ln under the mentioned restrictions, where L is one of the 15 basic monomodal logics. We show that, for n ≥ 2: a) the satisfiability problem of sets of Horn modal clauses in K5n, KD5n, K45n, and KD45n is PSPACEcomplete; b) the satisfiability problem of sets of Horn modal clauses with modal depth bounded by k ≥ 2 in Kn, KBn, K5n, K45n, KB5n is NPcomplete, and in KDn, Tn, KDBn, Bn,
On the Modularity of Theories
 IN ADVANCES IN MODAL LOGIC
, 2004
"... In this paper we give the notion of modularity of a theory and analyze some of its properties, especially for the case of action theories in reasoning about actions. We propose algorithms to check whether a given action theory is modular and that also make it modular, if needed. Completeness, correc ..."
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Cited by 7 (7 self)
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In this paper we give the notion of modularity of a theory and analyze some of its properties, especially for the case of action theories in reasoning about actions. We propose algorithms to check whether a given action theory is modular and that also make it modular, if needed. Completeness, correctness and termination results are demonstrated.
Metatheory of actions: beyond consistency
"... Traditionally, consistency is the only criterion for the quality of a theory in logicbased approaches to reasoning about actions. This work goes beyond that and contributes to the metatheory of actions by investigating what other properties a good domain description should have. We state some metath ..."
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Cited by 7 (4 self)
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Traditionally, consistency is the only criterion for the quality of a theory in logicbased approaches to reasoning about actions. This work goes beyond that and contributes to the metatheory of actions by investigating what other properties a good domain description should have. We state some metatheoretical postulates concerning this sore spot. When all postulates are satisfied we call the action theory modular. Besides being easier to understand and more elaboration tolerant in McCarthy’s sense, modular theories have interesting properties. We point out the problems that arise when the postulates about modularity are violated, and propose algorithmic checks that can help the designer of an action theory to overcome them.
Simulating Polyadic Modal Logics by Monadic Ones
 Journal of Symbolic Logic
, 2001
"... We define an interpretation of modal languages with polyadic operators in modal languages that use monadic operators (diamonds) only. We also define a simulation operator which associates a logic in the diamond language with each logic in the language with polyadic modal connectives. We prove that t ..."
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Cited by 6 (2 self)
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We define an interpretation of modal languages with polyadic operators in modal languages that use monadic operators (diamonds) only. We also define a simulation operator which associates a logic in the diamond language with each logic in the language with polyadic modal connectives. We prove that this simulation operator transfers several useful properties of modal logics, such as finite/recursive axiomatizability, frame completeness and the finite model property, canonicity and firstorder definability.
Analytic Tableau Systems for Propositional Bimodal Logics of Knowledge and Belief
 Proceedings of TABLEAUX 2002, LNAI 2381
, 2002
"... We give sound and complete analytic tableau systems for the propositional bimodal logics KB , KB C , KB 5 , and KB 5C . These logics have two universal modal operators K and B , where K stands for knowing and B stands for believing. The logic KB is a combination of the modal logic S5 (for K ) an ..."
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Cited by 4 (4 self)
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We give sound and complete analytic tableau systems for the propositional bimodal logics KB , KB C , KB 5 , and KB 5C . These logics have two universal modal operators K and B , where K stands for knowing and B stands for believing. The logic KB is a combination of the modal logic S5 (for K ) and KD45 (for B ) with the interaction axioms I : K ! B and C : B ! K B . The logics KB C , KB 5 , KB 5C are obtained from KB respectively by deleting the axiom C (for KB C ), the axioms 5 (for KB 5 ), and both of the axioms C and 5 (for KB 5C ). As analytic sequentlike tableau systems, our calculi give simple decision procedures for reasoning about both knowledge and belief in the mentioned logics.
Transfer Results for Hybrid Logic  Part I: the case without satisfaction operators
 Journal of Logic and Computation
, 2004
"... For every Kripke complete modal logic L we define its hybrid companion LH . For a reasonable class of logics, we present a satisfiabilitypreserving translation from LH to L. We prove that for this class of logics, complexity, (uniform) interpolation, finite axiomatization transfer from L to LH . ..."
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Cited by 3 (3 self)
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For every Kripke complete modal logic L we define its hybrid companion LH . For a reasonable class of logics, we present a satisfiabilitypreserving translation from LH to L. We prove that for this class of logics, complexity, (uniform) interpolation, finite axiomatization transfer from L to LH .
Combining Equational Theories Sharing NonCollapseFree Constructors
 Frontiers of Combining Systems, volume 1794 of Lecture Notes in Arti Intelligence
, 1999
"... In a previous work, we describe a method to combine decision procedures for the word problem for theories sharing constructors. One of the requirements of our combination method is that constructors be collapsefree. This paper removes that requirement by modifying the method so that it applies t ..."
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Cited by 3 (2 self)
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In a previous work, we describe a method to combine decision procedures for the word problem for theories sharing constructors. One of the requirements of our combination method is that constructors be collapsefree. This paper removes that requirement by modifying the method so that it applies to noncollapsefree constructors as well. This broadens the scope of our combination results considerably, for example in the direction of equational theories corresponding to modal logics.
On Axiomatic Products of PDL and S5: Substitution Tests And Knowledge
 Bull. Section Logic
, 2002
"... this paper concerns the uncertainty as to how substitutivity should be de ned in the product of PDL and S5. Because PDL has a twosorted language over actions and propositions, a key question is the following. In axiom schemata, do we allow substitution of all action terms into action variables, or ..."
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Cited by 2 (2 self)
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this paper concerns the uncertainty as to how substitutivity should be de ned in the product of PDL and S5. Because PDL has a twosorted language over actions and propositions, a key question is the following. In axiom schemata, do we allow substitution of all action terms into action variables, or do be allow only substitution of atomic action terms into action variables? If the answer is `yes' we speak of full substitutivity, whereas if the answer is `no' we speak of weak substitutivity. For PDL we can prove that weak substitutivity implies full substitutivity. (1) We regard this as a good property, because it allows us to reason about all actions in a uniform way