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A tableau calculus for minimal modal model generation
"... Model generation and minimal model generation is useful for fault analysis, verification of systems and validation of data models. Whereas for classical propositional and firstorder logic several model minimization approaches have been developed and studied, for nonclassical logic the topic has be ..."
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Model generation and minimal model generation is useful for fault analysis, verification of systems and validation of data models. Whereas for classical propositional and firstorder logic several model minimization approaches have been developed and studied, for nonclassical logic the topic has been much less studied. In this paper we introduce a minimal model generation calculus for multimodal logic K(m) and extensions of K(m) with the axioms T and B. The calculus provides a method to generate all and only minimal modal Herbrand models, and each model is generated exactly once. A novelty of the calculus is a nonstandard complement splitting rule designed for minimal model generation. Experiments show the rule has the added benefit of reducing the search space.
Developing Modal Tableaux and Resolution Methods via FirstOrder Resolution
"... abstract. This paper explores the development of calculi using different proof methods for propositional dynamic modal logics. Dynamic modal logics are PDLlike extended modal logics which are closely related to description logics. We show how tableau systems, modal resolution systems and RasiowaSi ..."
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abstract. This paper explores the development of calculi using different proof methods for propositional dynamic modal logics. Dynamic modal logics are PDLlike extended modal logics which are closely related to description logics. We show how tableau systems, modal resolution systems and RasiowaSikorski systems, which are dual tableau systems, can be developed and studied by using standard principles and methods of firstorder theorem proving. We translate modal logic reasoning problems to firstorder clausal form and then use a suitable refinement of resolution to construct and mimic derivations using the desired proof method. The inference rules of the calculus can then be read off from the clausal form used.
Deciding ALBO with Tableau
"... Abstract. This paper presents a tableau approach for deciding description logics outside the scope of OWL DL and current stateoftheart tableaubased description logic systems. In particular, we de ne a sound and complete tableau calculus for the description logic ALBO and show that it provides a ..."
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Abstract. This paper presents a tableau approach for deciding description logics outside the scope of OWL DL and current stateoftheart tableaubased description logic systems. In particular, we de ne a sound and complete tableau calculus for the description logic ALBO and show that it provides a basis for decision procedures for this logic and numerous other description logics. ALBO is the extension of ALC with the Boolean role operators, inverse of roles, domain and range restriction operators and it includes full support for objects (nominals). ALBO is a very expressive description logic which is NExpTime complete and subsumes Boolean modal logic and the twovariable fragment of rstorder logic. An important novelty is the use of a versatile, unrestricted blocking rule as a replacement for standard loop checking mechanisms implemented in description logic systems. Our decision procedure is implemented in the MetTeL system. 1
MetTeL2: Towards a tableau prover generation platform
 In these proceedings
, 2012
"... This paper introduces MetTeL 2, a tableau prover generator producing Java code from the specification of a logical syntax and a tableau calculus. It is intended to provide an easy to use system for nontechnical users and allow technical users to extend the generated implementations. 1 ..."
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This paper introduces MetTeL 2, a tableau prover generator producing Java code from the specification of a logical syntax and a tableau calculus. It is intended to provide an easy to use system for nontechnical users and allow technical users to extend the generated implementations. 1
Modal Satisfiability via SMT Solving
"... Modal logics extend classical propositional logic, and they are robustly decidable. Whereas most existing decision procedures for modal logics are based on tableau constructions, we propose a framework for obtaining decision procedures by adding instantiation rules to standard SAT and SMT solvers. ..."
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Modal logics extend classical propositional logic, and they are robustly decidable. Whereas most existing decision procedures for modal logics are based on tableau constructions, we propose a framework for obtaining decision procedures by adding instantiation rules to standard SAT and SMT solvers. Soundness, completeness, and termination of the procedures can be proved in a uniform and elementary way for the basic modal logic and some extensions.
Automated Reasoning in Deontic Logic?
"... Abstract. Deontic logic is a very well researched branch of mathematical logic and philosophy. Various kinds of deontic logics are discussed for different application domains like argumentation theory, legal reasoning, and acts in multiagent systems. In this paper, we show how standard deontic log ..."
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Abstract. Deontic logic is a very well researched branch of mathematical logic and philosophy. Various kinds of deontic logics are discussed for different application domains like argumentation theory, legal reasoning, and acts in multiagent systems. In this paper, we show how standard deontic logic can be stepwise transformed into description logic and DLclauses, such that it can be processed by Hyper, a high performance theorem prover which uses a hypertableau calculus. Two use cases, one from multiagent research and one from the development of normative system are investigated.
Solving the $100 Modal Logic Challenge
"... We present the theoretical foundation, design and implementation of a system that automatically determines the subset relation between two given axiomatizations of propositional modal logics. This is an open problem for automated theorem proving. Our system solves all but six out of 121 instances f ..."
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We present the theoretical foundation, design and implementation of a system that automatically determines the subset relation between two given axiomatizations of propositional modal logics. This is an open problem for automated theorem proving. Our system solves all but six out of 121 instances formed from 11 common axiomatizations of seven modal logics. Thus, although the problem is undecidable in general, our approach is empirically successful in practically relevant situations. Key words: Modal Logic, $100 challenge, subset relationship 1 Introduction and Related Work Modal logics are extensions of classical logic that handle the concept of modalities. Modern modal logic was founded by Clarence Irving Lewis in his 1910 Harvard thesis, and further developed in a series of scholarly articles beginning in 1912. In his book Symbolic Logic (with C. H. Langford), he introduced the