1,436 research outputs found
An Upper Bound on the Complexity of Recognizable Tree Languages
The third author noticed in his 1992 PhD Thesis [Sim92] that every regular
tree language of infinite trees is in a class
for some natural number , where is the game quantifier. We
first give a detailed exposition of this result. Next, using an embedding of
the Wadge hierarchy of non self-dual Borel subsets of the Cantor space
into the class , and the notions of Wadge degree
and Veblen function, we argue that this upper bound on the topological
complexity of regular tree languages is much better than the usual
Rough sets theory and uncertainty into information system
This article is focused on rough sets approach to expression of uncertainty into information system. We assume that the data are presented in the decision table and that some attribute values are lost. At first the theoretical background is described and after that, computations on real-life data are presented. In computation we wok with uncertainty coming from missing attribute values
Coq Modulo Theory - Short Paper
International audienceCoq Modulo Theory (CoqMT) is an extension of the Coq proof assistant incorporating, in its computational mechanism, validity entailment for user-defined first-order equational theories. Such a mechanism strictly enriches the system (more terms are typable), eases the use of dependent types and provides more automation during the development of proofs. CoqMT improves over the Calculus of Congruent Inductive Constructions by getting rid of various restrictions and simplifying the type-checking algorithm and the integration of first-order decision procedures
Building Decision Procedures in the Calculus of Inductive Constructions
It is commonly agreed that the success of future proof assistants will rely
on their ability to incorporate computations within deduction in order to mimic
the mathematician when replacing the proof of a proposition P by the proof of
an equivalent proposition P' obtained from P thanks to possibly complex
calculations. In this paper, we investigate a new version of the calculus of
inductive constructions which incorporates arbitrary decision procedures into
deduction via the conversion rule of the calculus. The novelty of the problem
in the context of the calculus of inductive constructions lies in the fact that
the computation mechanism varies along proof-checking: goals are sent to the
decision procedure together with the set of user hypotheses available from the
current context. Our main result shows that this extension of the calculus of
constructions does not compromise its main properties: confluence, subject
reduction, strong normalization and consistency are all preserved
Towards a Proof Theory of G\"odel Modal Logics
Analytic proof calculi are introduced for box and diamond fragments of basic
modal fuzzy logics that combine the Kripke semantics of modal logic K with the
many-valued semantics of G\"odel logic. The calculi are used to establish
completeness and complexity results for these fragments
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