Download Automated Reasoning with Analytic Tableaux and Related by Maria Paola Bonacina, Moa Johansson (auth.), Kai Brünnler, PDF

By Maria Paola Bonacina, Moa Johansson (auth.), Kai Brünnler, George Metcalfe (eds.)

This publication constitutes the refereed complaints of the twentieth overseas convention on computerized Reasoning with Analytic Tableaux and comparable equipment, TABLEAUX 2011, held in Bern, Switzerland, in July 2011.The sixteen revised study papers provided including 2 procedure descriptions have been conscientiously reviewed and chosen from 34 submissions. The papers disguise many subject matters within the wide selection of functions of tableaux and comparable equipment resembling analytic tableaux for varied logics, similar strategies and ideas, comparable tools, new calculi and techniques for theorem proving in classical and non-classical logics, in addition to platforms, instruments, implementations and purposes; all with a different specialize in and software program verifications, semantic applied sciences, and information engineering.

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Additional info for Automated Reasoning with Analytic Tableaux and Related Methods: 20th International Conference, TABLEAUX 2011, Bern, Switzerland, July 4-8, 2011. Proceedings

Sample text

We present here CSymLean, the first theorem-prover for CSL interpreted on symmetric minspaces. It is a Prolog implementation of a labelled tableau calculus recently proposed for this logic, and it is inspired by the Lean methodology. 1 The Logic CSL CSL is a propositional modal logic introduced by Sheremet, Tishkovsky, Wolter and Zakharyaschev for reasoning about the comparative similarity between concepts and/or objects [4]. In CSL one can formulate assertions of the form “objects A are more similar to B than to C”.

The problem is co-semi-decidable and decision procedures of “reasonable” complexity can be defined for some interesting classes (see [2] for details). A simple example is the following schema: p0 ∧ pn+1 ∧ ni=0 (pi ⇔ ¬pi+1 ), that is satisfiable if and only if n is odd. g. for n ← 0: p0 ∧ p1 ∧ (p0 ⇔ ¬p1 ), or for n ← 1: p0 ∧ p2 ∧ (p0 ⇔ ¬p1 ) ∧ (p1 ⇔ ¬p2 ). A SAT-solver can determine whether the formula is satisfiable or unsatisfiable for a given value of n and a model can be found (if it exists) by enumerating all possible values (n ← 0, 1, 2, .

Since we only deal with fully-structural systems, it is most convenient to define sequents using sets: Definition 1. A signed formula is an expression of the form f:ψ or t:ψ, where ψ is a formula. A sequent is a finite set of signed formulas. We shall usually employ the usual sequent notation Γ ⇒ Δ, where Γ and Δ are finite sets of formulas. Γ ⇒ Δ is interpreted as {f:ψ | ψ ∈ Γ } ∪ {t:ψ | ψ ∈ Δ}. g. Γ, ϕ instead of Γ ∪ {ϕ}, and Γ ⇒ instead of Γ ⇒ ∅. Definition 2. An L-substitution is a function σ : F rmL → F rmL , such that σ( (ψ1 , .

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