By Maria Paola Bonacina, Moa Johansson (auth.), Kai Brünnler, George Metcalfe (eds.)
This publication constitutes the refereed court cases of the twentieth foreign convention on automatic Reasoning with Analytic Tableaux and comparable tools, TABLEAUX 2011, held in Bern, Switzerland, in July 2011.The sixteen revised examine papers provided including 2 process descriptions have been rigorously reviewed and chosen from 34 submissions. The papers conceal many subject matters within the wide selection of functions of tableaux and comparable tools akin to analytic tableaux for numerous logics, similar strategies and ideas, similar equipment, new calculi and strategies for theorem proving in classical and non-classical logics, in addition to platforms, instruments, implementations and functions; all with a different specialize in and software program verifications, semantic applied sciences, and data 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
Given a set μ of signed formulas, we denote by frm[μ] the set of (ordinary) formulas appearing in μ, and by sub[μ] the set of subformulas of the formulas of frm[μ]. frm and sub are extended to sets of sets of signed formulas in the obvious way. Given a set E of formulas, a formula ψ (resp. sequent s) is called an E-formula (E-sequent) if ψ ∈ E (frm[s] ⊆ E). 1 Many eﬀorts have been devoted to characterize cut-free sequent systems. For example, a semantic characterization of cut-admissibility was the subject of .
It is parameterized by a simpliﬁcation function which is a function replacing a schema by a set of schemata (interpreted as a disjunction) in such a way that satisﬁability is preserved. Definition 1. Let φ be a schema and let Ψ be a set of schemata. We write φ Ψ iﬀ the following conditions hold: Schemata of SMT-Problems 33 1. For every I ∈ T , if I |= φ then there exists ψ ∈ Ψ such that I |= ψ. 2. For every I ∈ T , if there exists ψ ∈ Ψ such that I |= ψ then there exists an J I interpretation J ∈ T such that J |= φ and n = n .
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 . In CSL one can formulate assertions of the form “objects A are more similar to B than to C”. This type of assertions may be added to an ontology to express qualitative comparisons between concepts.