By Franz Baader, Ulrike Sattler (auth.), Roy Dyckhoff (eds.)
This booklet constitutes the refereed lawsuits of the foreign convention on computerized Reasoning with Analytic Tableaux and comparable tools, 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 incorporated are three invited lectures and six nonclassical procedure comparisons. All present matters surrounding the mechanization of reasoning with tableaux and comparable equipment are addressed - starting from theoretical foundations to implementation, structures improvement, and functions, in addition to protecting a extensive number of logical calculi.
Read or Download Automated Reasoning with Analytic Tableaux and Related Methods: International Conference, TABLEAUX 2000, St Andrews, Scotland, UK, July 3-7, 2000 Proceedings PDF
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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
Now, I assigns to a relation symbol R of type n1 , n2 , . . , nk a mapping on G such that t1 , . . , tk ∈ I(R)(σ) iﬀ σ R(t1 , . . , tk ) occurs on θ. This completes the deﬁnition of a model, call it M. Actually, the equality symbol may not be interpreted by equality, but leaving this aside for the moment, one can show by standard methods involving an induction on formula degree that, for any valuation v: – If σ Φ occurs on θ then M, σ – If σ ¬Φ occurs on θ then M, σ v Φ. v Φ. The valuation v can be arbitrary because free variables do not occur in tableaus.
In this section I’ll sketch soundness and completeness arguments for the tableau system, as well as give a proof for Proposition 1. Nothing is given in much detail, because proofs are straightforward adaptations of what are, by now, fairly standard arguments. 1 Soundness Soundness is by the usual tableau method. One deﬁnes a notion of satisﬁability for preﬁxed formulas—a set S is satisﬁable if there is a model M, a mapping m assigning to each preﬁx σ a possible world m(σ) of M, and a formula Φ is true at world m(σ) of M whenever σ Φ ∈ S.
11 A Derivation Example The example given here is a derivation of ¬✸[LOCATION ∧ (↓JOBNUMBER = 1) ∧ (↓WHERE = Away)] (10) from the axioms of Section 9. It establishes that ✸[LOCATION ∧ (↓JOBNUMBER = 1) ∧ (↓WHERE = Away)] cannot be inserted into the database, because it violates an integrity constraint. Before presenting the derivation itself, here is a derived rule that will shorten the presentation. Modality and Databases 35 Derived Rule Suppose τ is an individual concept constant symbol or parameter.