Baader, F. and Tobies, S. 2001. The inverse method implements the automata approach for modal satisfiability. In IJCAR '01: Proceedings of the First International Joint Conference on Automated Reasoning. Springer-Verlag, London, UK, 92--106.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....automaton that accepts all tree models of the formula. Second, the automaton is tested for non emptiness, i.e. does it accept some tree. The algorithms described in [21] combine the two steps and apply the non emptiness test without explicitly constructing the automaton. As was pointed out in [28, 2], the inverse method described in [37] can also be viewed as an implementation of the automata theoretic approach that avoids an explicit automata construction. The logic K is simple enough for the automaton non emptiness test to consist of a single fixpoint computation. This computation starts ....

F. Baader and S. Tobies. The inverse method implements the automata approach for modal satisfiability. In Proc. of IJCAR'01, volume 2083 of LNAI, pages 92--106.

.... backward modalities f[i] i] hii; hii : i 1g augmented with the universal modality [U ] More interestingly, this logic can be then viewed as an EXPTIME complete pivot logic between regular grammar logics with converse and GF and many decision procedures exist for it (see e.g. [DM00,HS00,BT01]) hii is also noted P i (existential past time operator) and [i] is also noted H i (universal past time operator) Let S be a regular, symmetric semi Thue system and let be an L formula in negative normal form (NNF) Let us de ne t( by induction on the subformulae of . ....

F. Baader and S. Tobies. The inverse method implements the automata approach for modal satis ability. In A. Leitsch, R. Gore, and T. Nipkow, editors, IJCAR'01, volume 2083 of Lecture Notes in Arti cial Intelligence, pages 92-106. Springer, 2001.

....to a tree automaton that accepts all tree models of the formula. Second, the automaton is tested for non emptiness, i.e. does it accept some tree. In our approach, we combine the two steps and apply the non emptiness test without explicitly constructing the automaton. As was pointed out in [3], the inverse method described in [30] can also be viewed as an implementation of the automatatheoretic approach that avoids an explicit automata construction. The logic K is simple enough for the automaton non emptiness test to consist of a single fixpoint computation. This computation starts ....

F. Baader and S. Tobies. The inverse method implements the automata approach for modal satisfiability. In Proc. of IJCAR-01, volume 2083 of LNCS. Springer Verlag, 2001.

....[ f 2 QG j g, and for a set S of sequents we de ne [ S] S 2S [ The following theorem, which is one of the main contributions of this paper, establishes the correspondence between the emptiness test and IC G . Its proof will be sketched in the remainder of this section (see [3] for details) Theorem 2 (ICG and the emptiness test mutually simulate each other) Let Q 0 , S 0 , B, and be de ned as above. 1. Let Q be a set of states such that Q 0 B Q. Then there exists a set of sequents S with S 0 S and Q [ S] 2. Let S be a set of sequents such that S 0 ....

.... the selection function as de ned above. Let = f g or = 2; i 3 with 2 paths and a 3 path , all of equal modal length. If T , as de ned in the proof of Lemma 4, is generated using select as selection function, then every node of T is compact. The proof of this lemma can be found in [3]. It is similar to the proof of Lemma 5.8.3 in [19] Given this lemma, it is easy to show that the construction employed in the proof of Lemma 4 also works for IC G , provided that we restrict the set as in Lemma 6: Lemma 7. Let = f g or = 2; i 3 with 2 paths and a 3 path all of ....

F. Baader and S. Tobies. The inverse method implements the automata approach for modal satisability. LTCS-Report 01-03, LuFG Theoretical Computer Science, RWTH Aachen, Germany, 2001. See http://www-lti.informatik.rwth-aachen.de/Forschung/Reports.html.

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F. Baader and S. Tobies. The inverse method implements the automata approach for modal satisability. LTCS-Report 01-03, LuFG Theoretical Computer Science, RWTH Aachen, Germany, 2001. See http://wwwlti. informatik.rwth-aachen.de/Forschung/Reports.html.

No context found.

Baader, F. and Tobies, S. 2001. The inverse method implements the automata approach for modal satisfiability. In IJCAR '01: Proceedings of the First International Joint Conference on Automated Reasoning. Springer-Verlag, London, UK, 92--106.

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BAADER F., TOBIES S., "The inverse method implements the automata approach for modal satisfiability", report num. LTCS-Report 01-03, 2001, Research group for theoretical computer science, Aachen university of Technology.

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