By Maria Paola Bonacina, Moa Johansson (auth.), Kai Brünnler, George Metcalfe (eds.)
This e-book constitutes the refereed lawsuits of the twentieth overseas convention on computerized Reasoning with Analytic Tableaux and comparable tools, TABLEAUX 2011, held in Bern, Switzerland, in July 2011.The sixteen revised examine papers provided including 2 method descriptions have been conscientiously reviewed and chosen from 34 submissions. The papers disguise many subject matters within the wide variety of functions of tableaux and similar equipment resembling analytic tableaux for varied logics, comparable concepts and ideas, comparable tools, new calculi and strategies for theorem proving in classical and non-classical logics, in addition to platforms, instruments, implementations and purposes; all with a unique specialise in and software program verifications, semantic applied sciences, and information engineering.
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Extra info for Automated Reasoning with Analytic Tableaux and Related Methods: 20th International Conference, TABLEAUX 2011, Bern, Switzerland, July 4-8, 2011. Proceedings
A schema is iteration-free iﬀ it contains no iterated connective or and parameter-free if it contains no occurrence of n. A sentence is a schema that is both iteration-free and parameter-free. Such a schema may be viewed as a standard (quantiﬁer-free) formula in the usual sense (with function symbols indexed by natural numbers), but we prefer not to use the word “formula” to avoid confusions. n For instance φ1 : i=0 (ai+1 ≈ f (bi ) ∧ bi+1 ≈ g(ai )), φ2 : an+1 ≈ f (bn ) ∧ 3 bn+1 ≈ g(an ), φ3 : i=0 (ai+1 ≈ f (bi ) ∧ bi+1 ≈ g(ai )) and φ4 : a1 ≈ f (b0 ) ∧ b1 ≈ g(a0 ) are schemata.
Fr Abstract. The logic CSL of comparative concept similarity has been introduced by Sheremet, et al. to capture a form of qualitative similarity comparison. 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 .
Obviously this rule preserves equivalence. A set of schemata is ﬁnite up to contraction if its normal form by the previous rule is ﬁnite. Theorem 3. Let L be a stably decomposable frame. If φ ∈ S(L) then Eρ∗ ◦unfold (φ) is ﬁnite up to contraction3 . Thus the satisﬁability problem is decidable for S(L). 4 Examples of Stably Decomposable Frames Theorems 2 and 3 deﬁne a procedure for deciding the satisﬁability of schemata in S(L). However, it relies on the fact that L is stably decomposable, and on the 2 3 See Deﬁnition 4 for the notion of S(L)-preserving function.
Automated Reasoning with Analytic Tableaux and Related Methods: 20th International Conference, TABLEAUX 2011, Bern, Switzerland, July 4-8, 2011. Proceedings by Maria Paola Bonacina, Moa Johansson (auth.), Kai Brünnler, George Metcalfe (eds.)