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12
Strongly Analytic Tableaux for Normal Modal Logics
, 1994
"... A strong analytic tableau calculus is presentend for the most common normal modal logics. The method combines the advantages of both sequentlike tableaux and prefixed tableaux. Proper rules are used, instead of complex closure operations for the accessibility relation, while non determinism and cu ..."
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Cited by 48 (13 self)
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A strong analytic tableau calculus is presentend for the most common normal modal logics. The method combines the advantages of both sequentlike tableaux and prefixed tableaux. Proper rules are used, instead of complex closure operations for the accessibility relation, while non determinism and cut rules, used by sequentlike tableaux, are totally eliminated. A strong completeness theorem without cut is also given for symmetric and euclidean logics. The system gains the same modularity of Hilbertstyle formulations, where the addition or deletion of rules is the way to change logic. Since each rule has to consider only adjacent possible worlds, the calculus also gains efficiency. Moreover, the rules satisfy the strong Church Rosser property and can thus be fully parallelized. Termination properties and a general algorithm are devised. The propositional modal logics thus treated are K, D, T, KB, K4, K5, K45, KDB, D4, KD5, KD45, B, S4, S5, OM, OB, OK4, OS4, OM + , OB + , OK4 + ,...
Cutfree Sequent and Tableau Systems for Propositional Diodorean Modal Logics
"... We present sound, (weakly) complete and cutfree tableau systems for the propositional normal modal logics S4:3, S4:3:1 and S4:14. When the modality 2 is given a temporal interpretation, these logics respectively model time as a linear dense sequence of points; as a linear discrete sequence of po ..."
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Cited by 20 (3 self)
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We present sound, (weakly) complete and cutfree tableau systems for the propositional normal modal logics S4:3, S4:3:1 and S4:14. When the modality 2 is given a temporal interpretation, these logics respectively model time as a linear dense sequence of points; as a linear discrete sequence of points; and as a branching tree where each branch is a linear discrete sequence of points. Although cutfree, the last two systems do not possess the subformula property. But for any given finite set of formulae X the "superformulae" involved are always bounded by a finite set of formulae X L depending only on X and the logic L. Thus each system gives a nondeterministic decision procedure for the logic in question. The completeness proofs yield deterministic decision procedures for each logic because each proof is constructive. Each tableau system has a cutfree sequent analogue proving that Gentzen's cutelimination theorem holds for these latter systems. The techniques are due to Hi...
Database Repairs and Analytic Tableaux
, 2003
"... In this article, we characterize in terms of analytic tableaux the repairs of inconsistent relational databases, that is databases that do not satisfy a given set of integrity constraints. For this purpose we provide closing and opening criteria for branches in tableaux that are built for database i ..."
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Cited by 7 (4 self)
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In this article, we characterize in terms of analytic tableaux the repairs of inconsistent relational databases, that is databases that do not satisfy a given set of integrity constraints. For this purpose we provide closing and opening criteria for branches in tableaux that are built for database instances and their integrity constraints. We use the tableaux based characterization as a basis for consistent query answering, that is for retrieving from the database answers to queries that are consistent v't the integrity constraints.
Building Models By Using Tableaux Extended By Equational Problems
, 1993
"... The problem of model construction is known to be a very important one. An extension of semantic tableaux (that can also be applied to the matings and to the connection method) allowing the building of models in a systematic way is presented. This approach is different from the usual one in semantic ..."
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Cited by 5 (2 self)
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The problem of model construction is known to be a very important one. An extension of semantic tableaux (that can also be applied to the matings and to the connection method) allowing the building of models in a systematic way is presented. This approach is different from the usual one in semantic tableaux, in which model construction is a byproduct of refutation failures (and this only in very particular cases). In fact, we incorporate in the object level, reasoning usually done in an ad hoc manner in the metalevel. Some of the rules introduced by this extension are essentially new. The impossibility of simulating them by the standard tableaux rules and their necessity in extending the class of captured models is shown. These rules and the modified classical ones are based on the use of equational problems. Equational problems are formulae containing only equalities and inequalities, connected by "and", "or" and quantified in a particular way. The method preserves the refutational...
Semianalytic Tableaux For Propositional Normal Modal Logics with Applications to Nonmonotonicity
, 1991
"... The propositional monotonic modal logics K45, K45D, S4:2, S4R and S4F elegantly capture the semantics of many current nonmonotonic formalisms as long as (strong) deducibility of A from a theory \Gamma; \Gamma ` A; allows the use of necessitation on the members of \Gamma: This is usually forbidden in ..."
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Cited by 5 (4 self)
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The propositional monotonic modal logics K45, K45D, S4:2, S4R and S4F elegantly capture the semantics of many current nonmonotonic formalisms as long as (strong) deducibility of A from a theory \Gamma; \Gamma ` A; allows the use of necessitation on the members of \Gamma: This is usually forbidden in modal logic where \Gamma is required to be empty, resulting in a weaker notion of deducibility. Recently, Marek, Schwarz and Truszczi'nski have given algorithms to compute the stable expansions of a finite theory \Gamma in various such nonmonotonic formalisms. Their algorithms assume the existence of procedures for deciding (strong) deducibility in these monotonic modal logics and consequently such decision procedures are important for automating nonmonotonic deduction. We first give a sound, (weakly) complete and cutfree, semianalytic tableau calculus for monotonic S4R, thus extending the cut elimination results of Schwarz for monotonic K45 and K45D. We then give sound and complete semi...
Labelling Ideality and Subideality
 Practical Reasoning, LNAI 1085
, 1996
"... In this paper we suggest ways in which logic and law may usefully relate; and we present an analytic proof system dealing with the Jones Porn's deontic logic of Ideality and Subideality, which offers some suggestions about how to embed legal systems in label formalism. ..."
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Cited by 3 (3 self)
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In this paper we suggest ways in which logic and law may usefully relate; and we present an analytic proof system dealing with the Jones Porn's deontic logic of Ideality and Subideality, which offers some suggestions about how to embed legal systems in label formalism.
An Analytic Tableaux based Characterization of Data Base Repairs for Consistent Query Answering
 In Working
, 2001
"... In this article, we characterize in terms of analytic tableaux the repairs of inconsistent relational data bases, that is data bases that do not satisfy a given set of integrity constraints. For this purpose we provide closing and opening criteria for branches in tableaux that are built for data ..."
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Cited by 2 (2 self)
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In this article, we characterize in terms of analytic tableaux the repairs of inconsistent relational data bases, that is data bases that do not satisfy a given set of integrity constraints. For this purpose we provide closing and opening criteria for branches in tableaux that are built for data base instances and their integrity constraints. We use the tableaux based characterization as a basis for algorithms for consistent query answering, that is for retrieving from the data base answers to queries that are consistent wrt the integrity constraints.
A Bridge Between Modal Logics and Contextual Reasoning
 In IJCAI95 International Workshop on Modeling Context in Knowledge Representation and Reasoning
, 1995
"... The goal of this paper is to present and discuss a simple and rather effective tableau calculus which combines modal logics of knowledge and belief with contextual reasoning. The system is made by a multiple combination. For modal proofs, it labels formulae as prefixed tableaux but uses message (kno ..."
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Cited by 2 (1 self)
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The goal of this paper is to present and discuss a simple and rather effective tableau calculus which combines modal logics of knowledge and belief with contextual reasoning. The system is made by a multiple combination. For modal proofs, it labels formulae as prefixed tableaux but uses message (knowledge) passing rules similar to those of sequentlike tableaux. For contextual deduction, it merges the metalevel information of the labelling system used by Multicontextual Languages with that used by Labelled Deductive Systems. Its semantics is also simple and intuitively based on a property of Kripke models. The resulting calculus (kClusters Tableaux) is effective for automated proofs, applicable to a wide range of modal logics, and adaptable to many search heuristics. It is also easy to use for proof presentation since its rule have intuitive epistemic interpretation (how knowledge and belief can be inherited up and down possible worlds). It is weak enough to satisfy a KB where two cons...
KClusters Tableaux  A Tool for Modal Logics and Inconsistent Belief Sets
 National Conferences
, 1994
"... The goal of this paper is to present a tableau calculus for propositional modal logics that is effective for automated proof search, easy to use for proof presentation, and applicable to a wide range of modal logics for knowledge representation. The calculus is also enhanced to provide a form of con ..."
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Cited by 1 (1 self)
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The goal of this paper is to present a tableau calculus for propositional modal logics that is effective for automated proof search, easy to use for proof presentation, and applicable to a wide range of modal logics for knowledge representation. The calculus is also enhanced to provide a form of contextual reasoning to deal with (classical) inconsistency. The basic tableau calculus (Single Step Tableaux) combines the advantage of both sequentlike tableaux and prefixed tableaux and eliminates the need of complex closure operations for the accessibility relation, nondeterminism and cut rules. Thus analiticy is provided together with a strong completeness theorem without cut. Single Step rules are rather efficient (they satisfy suitable locality principles) and also strongly confluent. They can thus be parallelized and adapted to many search heuristics. The system is then extended to cope with inconsistent belief sets (kCluster Tableaux), with a form of local reasoning. Yet it does not...
Semianalytic Tableaux For Propositional Modal Logics of Nonmonotonicity
, 1993
"... The propositional monotonic modal logics K45, K45D, S4:2, S4R and S4F elegantly capture the semantics of many current nonmonotonic formalisms as long as (strong) deducibility of A from a theory \Gamma; \Gamma ` A; allows the use of necessitation on the members of \Gamma: This is usually forbidden ..."
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Cited by 1 (0 self)
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The propositional monotonic modal logics K45, K45D, S4:2, S4R and S4F elegantly capture the semantics of many current nonmonotonic formalisms as long as (strong) deducibility of A from a theory \Gamma; \Gamma ` A; allows the use of necessitation on the members of \Gamma: This is usually forbidden in modal logic where \Gamma is required to be empty, resulting in a weaker notion of deducibility. Recently, Marek, Schwarz and Truszczi'nski have given algorithms to compute the stable expansions of a finite theory \Gamma in various such nonmonotonic formalisms. Their algorithms assume the existence of procedures for deciding (strong) deducibility in these monotonic modal logics and consequently such decision procedures are important for automating nonmonotonic deduction. We first give a sound, (weakly) complete and cutfree, semianalytic tableau calculus for monotonic S4R, thus extending the cut elimination results of Schwarz for monotonic K45 and K45D. We then give sound and co...