Trace Tableau = concrete trace unwinding + abstract looping trace tableau • automatic procedure to find proofs in the form of a looping trace tableau Figure 1: Data structures for causality-based model checking. the property of interest. The exploration algorithm proceeds by picking some forest leaf, and employing an applicable trace transformer, producing a number of further nodes. The explora...

We define a clause tableau calculus for MaxSAT, prove its soundness and completeness, and describe a tableau-based algorithm for MaxSAT. Given a multiset of clauses , the algorithm computes both the minimum number of clauses that can be falsified in , and an optimal assignment. We also describe how the algorithm can be extended to solve weighted MaxSAT and weighted partial MaxSAT.

We give the first ExpTime (optimal) tableau decision procedure for checking satisfiability of a knowledge base in the description logic ALC, not based on transformation that encodes ABoxes by nominals or terminology axioms. Our procedure can be implemented as an extension of the highly optimized tableau prover TGC [12] to obtain an efficient program for the mentioned satisfiability problem.

This paper tries to identify the basic problems encountered in handling equality in the semantic tableau framework, and to describe the state of the art in solving these problems. The two main paradigms for handling equality are compared: adding new tableau expansion rules and using E-uniication algorithms; their eecient implementation is discussed.

This paper introduces MetTeL2, a tableau prover generator producing Java code from the specification of a tableau calculus for a logical language. MetTeL2 is intended to provide an easy to use system for non-technical users and allow technical users to extend the generated

Consequence-based reasoners are typically significantly faster than tableau-based reasoners for ontology classification. However, for more expressive DL languages like ALCHO, consequence-based reasoners are not applicable, but tableau-based reasoners can sometimes require an unacceptably long time for large and complex ontologies. This paper presents a weakening and strengthening approach for c...

Recent experimental results have shown that the strength of resolution, the propositional DPLL procedure, the KSAT procedure for description logics, or related tableau-like implementations such as DLP, is due to reduction rules which propagate constraints and prune the search space. Yet, for first order logic such reduction rules are only known for resolution. The lack of reduction rules for fi...

Conditional functional dependencies (CFDs) have recently been proposed as a useful integrity constraint to summarize data semantics and identify data inconsistencies. A CFD augments a functional dependency (FD) with a pattern tableau that defines the context (i.e., the subset of tuples) in which the underlying FD holds. While many aspects of CFDs have been studied, including static analysis and...

The semantic valuations of classical logic, strong Kleene logic, the logic of paradox and the logic of first-degree entailment, all respect the Dunn conditions: we call them Dunn logics. In this paper, we study the interpolation properties of the Dunn logics and extensions of these logics to more expressive languages. We do so by relying on the Dunncalculus, a signed tableau calculus whose rule...