R. A. Schmidt. Resolution is a decision procedure for many propositional modal logics. In M. Kracht, M. de Rijke, H. Wansing, and M. Zakharyaschev, editors, Advances in Modal Logic, Volume 1, volume 87 of Lecture Notes, pages 189--208. CSLI Publications, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....an O( n:log n) into the decidable fragment FO 2 of classical logic. It is easy to see that the resulting formula is in the guarded fragment of classical logic, for which a proof procedure based on resolution is proposed in [19] Alternatively, after translating Grz into T, the techniques from [24] could also be used to translate T into classical logic. These are possibilities to obtain a decision procedure for Grz using theorem provers for classical logic. We are currently investigating whether this translation can be extended to first order Grz (FOGrz) where increasing, decreasing, and ....

R. Schmidt. Resolution is a decision procedure for many propositional modal logics. Technical Report MPI-I-97-2-002, Max-Planck-Institute Fur Informatik, 1997.

....implement and amenable to optimizations, so that it behaves well on practical instances of the decision problem. The most popular approaches for constructing decision procedures for modal logics are i) semantic tableaux and related methods [10, 2] ii) translations into classical rst order logics [15, 1]; and iii) reductions to the emptiness problem for certain (tree) automata [17, 14] Whereas highly optimized tableaux and translation approaches behave quite well in practice [11, 12] it is sometimes hard to obtain exact worst case complexity results using these approaches. For example, satis ....

R. A. Schmidt. Resolution is a decision procedure for many propositional modal logics. In M. Kracht, M. de Rijke, H. Wansing, and M. Zakharyaschev, editors, Advances in Modal Logic, Volume 1, volume 87 of Lecture Notes, pages 189-208. CSLI Publications, Stanford, 1998.

....and amenable to optimizations, such that it behaves well on practical instances of the decision problem. The most popular approaches for constructing decision procedures for modal logics are i) semantic tableaux and related methods [10, 2] ii) translations into classical rst order logics [15, 1]; and iii) reductions to the emptiness problem for certain (tree) automata [17, 14] Whereas highly optimized tableaux and translation approaches behave quite well in practice [11, 12] it is sometimes hard to obtain exact worstcase complexity results using these approaches. For example, satis ....

R. A. Schmidt. Resolution is a decision procedure for many propositional modal logics. In M. Kracht, M. de Rijke, H. Wansing, and M. Zakharyaschev, editors, Advances in Modal Logic, Volume 1, volume 87 of Lecture Notes, pages 189-208. CSLI Publications, Stanford, 1998.

.... be embedded into a decidable fragment of predicate logic [AvBN98] Hence, there are two general approaches for reasoning with KR : dedicated decision procedures [Lad77, SSS91, GS96] and the translation into first order logic followed by the application of an existing first order theorem prover [OS97, Sch97]. To compete with the dedicated algorithms, the second approach has to yield a decision procedure and it has This papers appeared in the Journal of Logic and Computation, Vol. 10 No. 99 47, pp. 1 22 2000. 1 to be efficient, because the dedicated algorithms usually have optimal worst case ....

R. A. Schmidt. Resolution is a decision procedure for many propositional modal logics: Extended abstract. In M. Kracht, M. de Rijke, H. Wansing, and M. Zakharyaschev, editors, Advances in Modal Logic '96. CLSI Publications, 1997.

.... can be embedded into a decidable fragment of predicate logic [AvBN98] Hence, there are two general approaches for reasoning with KR : dedicated decision procedures [Lad77, SSS91, GS96] and the translation into rst order logic followed by the application of an existing rst order theorem prover [OS97, Sch97]. To compete with the dedicated algorithms, the second approach has to yield a decision procedure and it has to be ecient, because the dedicated algorithms usually have optimal worst case complexity. For KR , the rst issue is solved and, regarding the complexity, experimental results show that ....

R. A. Schmidt. Resolution is a decision procedure for many propositional modal logics: Extended abstract. In M. Kracht, M. de Rijke, H. Wansing, and M. Zakharyaschev, editors, Advances in Modal Logic '96. CLSI Publications, 1997.

.... can be embedded into a decidable fragment of predicate logic [AvBN98] Hence, there are two general approaches for reasoning with KR : dedicated decision procedures [Lad77,SSS91,GS96] and the translation into first order logic followed by the application of an existing first order theorem prover [OS97,Sch97]. To compete with the dedicated algorithms, the second approach has to yield a decision procedure and it has to be efficient, because the dedicated algorithms usually have optimal worst case complexity. For KR , the first issue is solved and, regarding the complexity, experimental results show ....

R. A. Schmidt. Resolution is a decision procedure for many propositional modal logics: Extended abstract. In M. Kracht, M. de Rijke, H. Wansing, and M. Zakharyaschev, editors, Advances in Modal Logic '96. CLSI Publications, 1997.

....(which is stronger than mere equivalence of provability or semantics) that explicitly scoped calculus can be considered a purely proof theoretic optimization. Further, as in this paper, the explicitly scoped calculus can be studied fruitfully as a proof theoretic object in its own right (see (Schmidt, 1996) for another example) Example 3. Consider again the three theorems of example two. Proofs identical TREE CONSTRAINTS FOR NECESSITY 19 fffi = fffi axiom .a fffi a fffi fffi = fffi axiom .a fffi ; b fffi b fffi 2 .a fffi ; 2b fffi b fffi oe .a fffi ; a oe 2b ....

Schmidt, R. A. (1996). Resolution is a decision procedure for many propositional modal logics. In AiML.

....from Grz into the decidable fragment FO 2 of classical logic. It is easy to see that the resulting formula is in the guarded fragment of classical logic, for which a proof procedure based on resolution is proposed in [19] Alternatively, after translating Grz into T, the techniques from [24] could also be used to translate T into classical logic. These are possibilities to obtain a decision procedure for Grz using theorem provers for classical logic. We are currently investigating whether this translation can be extended to first order Grz (FOGrz) where increasing, decreasing, and ....

R. Schmidt. Resolution is a decision procedure for many propositional modal logics. Technical Report MPI-I-97-2-002, Max-Planck-Institute Fur Informatik, 1997.

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R. A. Schmidt. Resolution is a decision procedure for many propositional modal logics. In M. Kracht, M. de Rijke, H. Wansing, and M. Zakharyaschev, editors, Advances in Modal Logic, Volume 1, volume 87 of Lecture Notes, pages 189--208. CSLI Publications, 1998.

....have some pleasant properties. The class of modal algebras is representable (which follows by specialisation from J onsson and Tarski 1951 1952) The equational theory is decidable, and by a new result for modal logic, standard resolution provides a procedure for deciding the equational validity (Schmidt 1997). In contrast to knowledge representation, in computational linguistics decidability is not an essential prerequisite, on the contrary, some may argue, compared to first order logic, for example, the algebraic framework is expressively too weak for serious linguistic analysis. Indeed, there are ....

Schmidt, R. A. (1997), Resolution is a decision procedure for many propositional modal logics. To appear in Kracht, M., de Rijke, M., Wansing, H. and Zakharyaschev, M.

....for defining accessibility. Clauses of path logics are restricted in that only Skolem terms which are constants may occur and the prefix stability property holds. Ordinary resolution without any refinement strategies is a decision procedure for the path logics associated with K(m) and KT (m) [3]. Our decision procedure for S4 uses an a priori term depth bound. Availability: SPASS and a routine for the translation of modal formulae are available from http: www.mpi sb.mpg.de #hustadt mdp Advantages of the prover: SPASS is a fast and sophisticated state of the art first order theorem ....

.... propositional modal logics, including K, KT, and S4 and their multi modal versions, but notably also to some second order modal logics, like KM [2] A general result shows that any first order resolution theorem prover (with condensing) provides a decision procedure for a variety of modal logics [3]. Hardware: Sun Ultra 1 Model 170E (167 MHz UltraSPARC processor, 512 KB second level cache) 192 MB main memory. Results: On classes of provable formulae (in the first column) the combination of the optimised functional translation approach and SPASS has little di# culty. Notable exceptions ....

R. A. Schmidt. Resolution is a decision procedure for many propositional modal logics: Extended abstract. To appear in Proc. AiML'96, 1997.

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