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Abstract. Tableau and sequent calculi are the basis for most popular interactive theorem provers for formal verification. Yet, when it comes to automatic proof search, tableaux are often slower than Davis-Putnam, SAT procedures or other techniques. This is partly due to the absence of a bivalence principle (viz. the cut-rule) but there is another source of inefficiency: the lack of constraint propagation mechanisms.
1998 •
FaCT: The tests were performed using FaCT version 1.2. FaCT is a description logic classifier whose description language is a superset of K4 (m) and whose subsumption reasoning uses a sound and complete tableaux algorithm. FaCT employs a wide range of optimisations, in particular a form of dependency directed backtracking called backjumping which can significantly reduce the size of the search space [5].
1998 •
FaCT is a Description Logic classifier which has been implemented as a test-bed for a highly optimised tableaux satisfiability (subsumption) testing algorithm. The correspondence between modal and description logics also allows FaCT to be used as a theorem prover for the propositional modal logics K, KT, K4 and S4. Empirical tests have demonstrated the effectiveness of the optimised implementation and, in particular, of the dependency directed backtracking optimisation.
2000 •
We apply tableau methods to the problem of computing entailment in the nonmonotonic system of equilibrium logic, a generalisation of the inference relation associated with the stable model and answer set semantics for logic programs. We describe tableau calculi for the nonclassical logics underlying equilibrium entailment, namely here-and-there with strong negation and its strengthening classical logic with strong negation. A further tableau calculus is then presented for computing equilibrium entailment.
1998 •
Starting with a derivation in the refutation calculus CRIP of Pinto and Dyckhoff, we give a constructive algebraic method for determining the values of formulas of intuitionistic propositional logic in a counter-model. The values of compound formulas are computed point-wise from the values on atoms, in contrast to the non-local determination of forcing relations in a Kripke model based on classical reasoning.
1998 •
This paper introduces a tableau method for propositional interval temporal logic (ITL)[14]. Beyond the usual operators of linear temporal logic, ITL contains sequencing and iterative operators,';'and proj akin to programming combinators. Central to our approach is a normal form for the formulas of ITL, particularly ';'and proj, in terms of the '◯'operator of the logic.
2007 •
182 Ian Horrocks, Ullrich Hustadt, Ulrike Sattler, and Renate Schmidt axioms (background theories), and NExpTime-complete for Kn extended with converse modalities, graded modalities and nominals. Some may regard these results as discouraging and the question arises whether automated computation with such logics can be feasible in practice.
2005 •
Description Logics (DLs) are a family of logic based knowledge representation formalisms. Although they have a range of applications (eg, configuration and information integration), they are perhaps best known as the basis for widely used ontology languages such as OWL (now a W3C recommendation). This decision was motivated by a requirement that key inference problems be decidable, and that it should be possible to provide reasoning services to support ontology design and deployment.
We introduce a new Gentzen-style framework of grafted hypersequents that combines the formalism of nested sequents with that of hypersequents. To illustrate the potential of the framework, we present novel calculi for the modal logics K5 and KD5, as well as for extensions of the modal logics K and KD with the axiom for shift reflexivity. The latter of these extensions is also known as SDL+ in the context of deontic logic. All our calculi enjoy syntactic cut elimination and can be used in backwards proof search procedures of optimal complexity.
Journal of Applied Non-Classical Logics
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Theoretical Computer Science
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A tableau system for a first-order hybrid logic2007 •
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Investigations into the complexity of some propositional calculi1990 •