By Joachim Baran, Howard Barringer (auth.), Daniel Leivant, Ruy de Queiroz (eds.)
Welcome to the complaints of the 14th WoLLIC assembly, which used to be held in Rio de Janeiro, Brazil, July 2 - five, 2007. The Workshop on common sense, Language, details and Computation (WoLLIC) is an annual overseas discussion board on inter-disciplinary examine concerning formal good judgment, computing and programming concept, and usual language and reasoning. The WoLLIC conferences exchange among Brazil (and Latin the USA) and different nations, with the purpose of fostering curiosity in utilized good judgment between Latin Am- ican scientists and scholars, and facilitating their interplay with the foreign - plied common sense neighborhood. WoLLIC 2007 inquisitive about foundationsof computing and programming,novel c- putation types and paradigms, vast notions of evidence and trust, formal equipment in software program and improvement; logical techniques to traditional language and r- soning; logics of courses, activities and assets; foundational elements of data association, seek, ?ow, sharing, and safeguard. this system Committee for this assembly, inclusive of the 28 colleagues in this article, was once designed to advertise those inter-disciplinary and cross-disciplinary themes. Like its predecessors, WoLLIC 2007 incorporated invited talks and tutorials in addition to contributed papers. this system Committee got fifty two entire submissions (aside from 15 initial abstracts which didn't materialize). an intensive evaluate strategy via this system Committee, assisted by means of over 70 exterior reviewers, ended in the acc- tance of 21 papers for presentation on the assembly and inclusion in those complaints. The convention application additionally incorporated sixteen talks and tutorials by way of 10 fashionable invited audio system, who graciously authorized this system Committee’s invitation.
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Extra info for Logic, Language, Information and Computation: 14th International Workshop, WoLLIC 2007, Rio de Janeiro, Brazil, July 2-5, 2007. Proceedings
4. commutativity: T (x, y) = T (y, x), associativity: T (x, T (y, z)) = T (T (x, y), z), neutral element: T (x, 1) = x and monotonicity: If y ≤L z then T (x, y) ≤L T (x, z). Notice that for the lattice I in particular, this notion of t-norm coincides with the usual one. The well known G¨odel and weak t-norms (also known by minimum and drastic product t-norm ) can be generalized for arbitrary bounded lattice in a natural way. In particular, the G¨odel t-norm (TG ) coincides with ∧ itself and the weak t-norm is defined by 0 if x = 1 and y = 1 TW (x, y) = x ∧ y otherwise Analogously as we have a partial order on the set of t-norm we can establish a partial order on the set of all t-norms on a bounded lattice.
G. ¬p(x) ∨ p(f (x)), 44 H. Bensaid, R. Caferra, and N. Peltier which obviously entail a trivial “cycle”. In many cases, these cycles can be detected using simple syntactic criteria, and the corresponding I-terms can be introduced to describe the whole set of deducible clauses (here ¬p(x) ∨ p(f n (x)). In  a more general approach is proposed, using a sophisticated analysis on the proof tree in order to detect more complex cycles that are not explicitly generated by the proof procedure. The approach we investigate in this paper is diﬀerent: it is completely independent on the considered proof procedure and uses inductive generalization techniques instead of deduction.
Other resolution-based theorem provers could of course be used instead, with little programming eﬀort. Simplification: From Trees to I-Terms. The ﬁrst operation consists in compacting terms of the form f (f (f (f (. . a for example. The aim is to identify patterns (represented as contexts) that are iterated in the considered terms and clauses. One can view this process as a systematic (non deterministic) application of the following rules: – Context Creation. s where s is a subterm of t such that s = t and t[ ] denotes the context obtained by replacing any occurrence of s in t by .
Logic, Language, Information and Computation: 14th International Workshop, WoLLIC 2007, Rio de Janeiro, Brazil, July 2-5, 2007. Proceedings by Joachim Baran, Howard Barringer (auth.), Daniel Leivant, Ruy de Queiroz (eds.)