Automated Reasoning with Analytic Tableaux and Related by Franz Baader, Ulrike Sattler (auth.), Roy Dyckhoff (eds.)

By Franz Baader, Ulrike Sattler (auth.), Roy Dyckhoff (eds.)

This publication constitutes the refereed lawsuits of the overseas convention on automatic Reasoning with Analytic Tableaux and comparable equipment, TABLEAUX 2000, held in St Andrews, Scotland, united kingdom, in July 2000.
The 23 revised complete papers and a pair of process descriptions offered have been conscientiously reviewed and chosen from forty two submissions. additionally integrated are three invited lectures and six nonclassical process comparisons. All present matters surrounding the mechanization of reasoning with tableaux and related tools are addressed - starting from theoretical foundations to implementation, structures improvement, and purposes, in addition to masking a large number of logical calculi.

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Extra resources for Automated Reasoning with Analytic Tableaux and Related Methods: International Conference, TABLEAUX 2000, St Andrews, Scotland, UK, July 3-7, 2000 Proceedings

Example text

Since PHCnt has no global symmetries, it follows that the global symmetry rule cannot be employed in a refutation of this set of clauses. Thus any SR-I refutation of PHCnt must simply be a resolution refutation. Let φ be the assignment to the edge variables that results from matching all the tail vertices with other tail vertices (this can be done because all the tails are of even length).

Fortunately, for S5, the situation is somewhat simpler than it is for other modal logics since, to say X is valid in a model is just to say ✷X is true at some world of it. So, if we have a notion of local consequence, we can define a corresponding global consequence notion simply by introducing necessity symbols throughout. So, local consequence is all we need here. Definition 8 (Consequence). A closed formula X is a consequence of a set S of closed formulas if, in every model, X is true at each world at which all the members of S are true.

1 = 2), ¬(Home = Away), ¬(Adam = Eve), etc. 10 Tableaus Since consequence issues are important, a sound and complete proof procedure can be useful. Fortunately, standard tableau methods using prefixed formulas adapt quite naturally. Proofs, and derivations, will be of closed formulas. As usual, in order to handle existential quantifiers, parameters will be introduced. We can think of these as being additional constant symbols, added to the language for the purpose of proof construction. Since we have two kinds of quantifiers, object and concept, we will have two kinds of parameters as well.

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