ON SOME INTERPRETATIONS OF CLASSICAL LOGIC

In distinction from the well-known double-negation embeddings of the classical logic we consider some variants of single-negation embeddings and describe some classes of superintuitionistic first-order predicate logics in which the classical first-order calculus is interpretable in such a way. Also we find the minimal extensions of Heyting's logic in which the classical predicate logic can be embedded by means of these translations.     

Fock Theories and Quantum Logics

The notion of Fock theory is introduced in the framework of quantum logics, which are here orthomodular atomic lattices satisfying the covering property. It is shown that there are some fundamental facts concerning particles, which may be successfully discussed in this general context. One of these facts is to establish the theoretical conditions for considering particles as sharply defined entities. The other refers to the theoretical circumstances, which almost impose to consider that some particles have a structure, meaning they are composed from other particles. This last problem is strongly related with the conservative time evolutions.     

On the polynomial-space completeness of intuitionistic propositional logic

We present an alternative, purely semantical and relatively simple, proof of the Statman's result that both intuitionistic propositional logic and its implicational fragment are PSPACE-complete.This paper was supported by grant 401/01/0218 of the Grant Agency of the Czech Republic. % Mathematics Subject Classification (2000):     

Greechie Logics with Simple State Space Structure

We provide a simple algorithm for constructing Greechie logics whose states are convex linear combinations of two-valued states.     

基于吴方法的多值模型检验

大型复杂系统的开发过程中不可避免的涉及到非确定或不一致信息的处理,而多值模型检验作为经典模型检验的一种扩展,是处理和分析包含此类信息模型的一种有效手段.提出了一种系统化的多值逻辑(涵盖经典逻辑)的代数表示方法,使用吴方法的基本思想和框架实现复杂系统形式验证中基于多值逻辑的模型检验的代数化,建立了通过吴方法实现多值模型检验技术的整体框架.这种代数化的多值模型检验方法可以作为现有方法的有力补充.     

Analyzing completeness of axiomatic functional systems for temporal × modal logics

In previous works, we presented a modification of the usual possible world semantics by introducing an independent temporal structure in each world and using accessibility functions to represent the relation among them. Different properties ofthe accessibility functions (being injective, surjective, increasing, etc.) have been considered and axiomatic systems (called functional) which define these properties have been given. Only a few ofthese systems have been proved tobe complete. The aim ofthis paper is to make a progress in the study ofcompleteness for functional systems. For this end, we use indexes as names for temporal flows and give new proofs of completeness. Specifically, we focus our attention on the system which defines injectivity, because the system which defines this property without using indexes was proved to be incomplete in previous works. The only system considered which remains incomplete is the one which defines surjectivity, even ifwe consider a sequence ofnatural extensions ofthe previous one (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Categorical abstract algebraic logic: The categorical Suszko operator

Czelakowski introduced the Suszko operator as a basis for the development of a hierarchy of non‐protoalgebraic logics, paralleling the well‐known abstract algebraic hierarchy of protoalgebraic logics based on the Leibniz operator of Blok and Pigozzi. The scope of the theory of the Leibniz operator was recently extended to cover the case of, the so‐called, protoalgebraic π‐institutions. In the present work, following the lead of Czelakowski, an attempt is made at lifting parts of the theory of the Suszko operator to the π‐institution framework. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Existence of EF‐equivalent non‐isomorphic models

We prove the existence of pairs of models of the same cardinality λ which are very equivalent according to EF games, but not isomorphic. We continue the paper [4], but we do not rely on it. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fuzzy ontology representation using OWL 2

The need to deal with vague information in Semantic Web languages is rising in importance and, thus, calls for a standard way to represent such information. We may address this issue by either extending current Semantic Web languages to cope with vagueness, or by providing a procedure to represent such information within current standard languages and tools. In this work, we follow the latter approach, by identifying the syntactic differences that a fuzzy ontology language has to cope with, and by proposing a concrete methodology to represent fuzzy ontologies using OWL 2 annotation properties. We also report on some prototypical implementations: a plug-in to edit fuzzy ontologies using OWL 2 annotations and some parsers that translate fuzzy ontologies represented using our methodology into the languages supported by some reasoners.     

覆盖空间及粗糙集与拓扑的统一

引入覆盖空间,定义了其邻域、内部、闭包、测度等概念,研究了它们的性质.得出了粗糙集近似空间和拓扑空间都是具体覆盖空间的重要结论,从而用覆盖空间统一了粗糙集和拓扑.利用覆盖空间,得到了粗糙集和拓扑中更深刻的性质,从算子论和集合论的角度丰富和深化了粗糙集与拓扑的内容.