ISSN:1166-3081    

DOI:10.1080/11663081.1998.10510930

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

The palier explains the methods of approximation of set which were earlier put forth by the authors (1995a, 1995b) and by W. Marek and H. Rasiowa (1986). An essential part of this paper is devoted to the presentation of a certain calculus of rough sets and contextual rough sets in contextual spaces.

ISSN:1166-3081    

DOI:10.1080/11663081.1998.10510931

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

In this paper it is shown that a broad class of propositional logics can be interpreted in an equational logic based on fork algebras. This interpetability enables us to develop a fork-algebraic formalization of these logics and, as a consequence, to simulate non-classical means of reasoning with equational theories algebras.

ISSN:1166-3081    

DOI:10.1080/11663081.1998.10510932

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

The two main directions pursued in the present paper are the following. The first direction was (perhaps) started by Pigozzi in 1969. In [Mak 91] and [Mak 79] Maksimova proved that a normal modal logic (with a single unary modality) has the Craig interpolation property iff the corresponding class of algebras has the superamalgamation property. In this paper we extend Maksimova's theorem to normal multi-modal logics with arbitrarily many, not necessarily unary modalities, and to not necessarily normal multi-modal logics with modalities of ranks smaller than 2. To extend the characterization beyond multi-modal logics, we look at arbitrary algebraizable logics. We will introduce an algebraic property equivalent with the Craig interpolation property in algebraizable (and in strongly nice) logics, and prove that the superamalgamation property implies the Craig interpolation property. The problem of extending the characterization result to non-normal non-unary modal logics also will be discussed. In the second direction pursued herein: for non-normal modal logic with one unary modality Lemmon [Lem 66] gave a possible worlds semantics. Here we give a more general possible worlds semantics for not necessarily normal multi-modal logics with arbitrarily many not necessarily unary modalities. Strongly related to the above is the theorem, proved, e.g., in Jóns son-Tarski [JT 52] and Henkin-Monk-Tarski [HMT 71], that every normal Boolean algebra with operators (BAO) can be represented as a subalgebra of the complex algebra of some relational structure. We extend this result to not necessarily normal BAO's as follows. We define partial relational structures and show that every not necessarily normal BAO is embeddable into the complex algebra of a partial relational structure. This gives a possible worlds semantics for not necessarily normal multi-modal logics (with arbitrarily many, not necessarily unary modalities).

ISSN:1166-3081    

DOI:10.1080/11663081.1998.10510933

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

This paper gives a survey of known results related to computational devices (finite and push-down automata) recognising monadic generalised quantifiers infinite models. Some of these results are simple reinterpretations of descriptive-feasible correspondence theorems from finite-model theory. Additionally a new result characterizing monadic quantifiers recognized by push down automata is proven.

ISSN:1166-3081    

DOI:10.1080/11663081.1998.10510934

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

This paper presents an attempt to create a shell for generic interactive proof search and proof assistant software based on it.

ISSN:1166-3081    

DOI:10.1080/11663081.1998.10510935

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

A new type of calculi is proposed for a first order linear temporal logic. Instead of induction-type postulates the introduced calculi contain a similarity saturation principle, indicating some form of regularity in the derivations of the logic. In a finitary case we obtained the finite set of saturated sequents, showing that “nothing new” can be obtained continuing the derivation process. Instead of the ω-type rule of inference, an infinitary saturated calculus has an infinite set of saturated sequents, showing that only a “similar” sequents can be obtained continuing the dérivation process. The saturation calculi have some resemblance with resolution-like calculi.

ISSN:1166-3081    

DOI:10.1080/11663081.1998.10510936

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

After indicating why this is needed, the paper proves a non-triviality result for a paraconsistent theory containing arithmetic, naive truth and denotation predicates, and descriptions. The result is obtained by dualising a construction of Kroon. Its most notable feature is that there is a trivial object—one that has every property.

ISSN:1166-3081    

DOI:10.1080/11663081.1998.10510937

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

The instructionsbelow fall into three categories. The editor of the review would be grateful to authors for respecting these indications. At times, the length of this summary may attain a dozen lines. It is to be written in size 9 italic Times.

ISSN:1166-3081    

DOI:10.1080/11663081.1998.10510939

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

ISSN:1166-3081    

DOI:10.1080/11663081.1998.10510940

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor