摘要:

AbstractMIPC is a well‐known intuitionistic modal logic of Prior (1957) and Bull (1966). It is shown that every normal intuitionistic modal logicLover MIPC has the finite model property wheneverLis Kripke‐complete and univer

ISSN:0942-5616    

DOI:10.1002/malq.19990450402

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1999

数据来源: WILEY

摘要:

AbstractIn this paper we investigate conditions forLp‐computability which are in accordance with the classical Grzegorczyk notion of computability for a continuous function. For a given computable real numberp≥ 1 and a compact computable rectangle I ⊂ ℝq, we show that anLpfunctionf∈Lp(I) isLP‐computable if and only if (i)fis sequentially computable as a linear functional and (ii) theLp‐modulus function offis effectively continuous at the

ISSN:0942-5616    

DOI:10.1002/malq.19990450403

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1999

数据来源: WILEY

摘要:

AbstractIn order to modelize the reasoning of an intelligent agent represented by a posetT, H. Rasiowa introduced logic systems called “Approximation Logics”. In these systems a set of constants constitutes a fundamental tool. In this papers, we consider logic systems calledL′Twithout this kind of constants but limited to the case where T is a finite poset. We prove a weak deduction theorem. We introduce also an algebraic semantics using Hey ting algebra with operators. To prove the completeness theorem of theL′Tsystem with respect to the algebraic semantics, we use the method of H. Rasiowa and R. Sikorski for first order logic. In the propositional case, a corollary allows us to assert that it is decidable to know “if a propositional formula is valid”. We study also certain relations between theL′Tlogic and the intuitionistic and cla

ISSN:0942-5616    

DOI:10.1002/malq.19990450404

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1999

数据来源: WILEY

摘要:

AbstractWe define a class of so‐called ∑(n)‐sets as a natural closure of recursively enumerable setsWnunder the relation “∈” and study its

ISSN:0942-5616    

DOI:10.1002/malq.19990450405

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1999

数据来源: WILEY

摘要:

AbstractWe prove a completeness theorem for Kf, an extension of K by the operator ⋄fthat means “there exists a finite number of accessible worlds such that … is true, plus suitable axioms to rule it. This is done by an application of the method of consistency properties for modal systems as in [4] with suitable adaptations. Despite no graded modality is invoked here, we consider this work as pertaining to that area both because ⋄fis a definable operator in the graded infinitary system Kω10(see [4]), and because this idea was the original source for the development of graded mo

ISSN:0942-5616    

DOI:10.1002/malq.19990450406

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1999

数据来源: WILEY

摘要:

AbstractFor semi‐continuous real functions we study different computability concepts defined via computability of epigraphs and hypographs. We call a real functionflower semi‐computable of type one, if its open hypograph hypo(f) is recursively enumerably open in dom(f) × ℝ; we callflower semi‐computable of type two, if its closed epigraph Epi(f) is recursively enumerably closed in dom(f) × ℝ; we callflower semi‐computable of type three, if Epi(f) is recursively closed in dom(f) × ℝ. We show that type one and type two semi‐computability are independent and that type three semi‐computability plus effectively uniform continuity implies computability, which is false for type one and type two instead of type three. We show also that the integral of a type three semi‐computable real function on a computable interval is not

ISSN:0942-5616    

DOI:10.1002/malq.19990450407

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1999

数据来源: WILEY

摘要:

AbstractThe concept of Galois connection between power sets is generalized from the point of view of fuzzy logic. Studied is the case where the structure of truth values forms a complete residuated lattice. It is proved that fuzzy Galois connections are in one‐to‐one correspondence with binary fuzzy relations. A representation of fuzzy Galois connections by (classical) Galois connections is provi

ISSN:0942-5616    

DOI:10.1002/malq.19990450408

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1999

数据来源: WILEY

摘要:

AbstractOur investigation is concerned with the finite model property (fmp) with respect to admissible rules. We establish general sufficient conditions for absence of fmp w. r. t. admissibility which are applicable to modal logics containing K4: Theorem 3.1 says that no logic λ containing K4 with the co‐cover property and of width>2 has fmp w. r. t. admissibility. Surprisingly many, if not to say all, important modal logics of width>2 are within the scope of this theorem–K4 itself, S4, GL, K4.1, K4.2, S4.1, S4.2, GL.2, etc. Thus the situation is completely opposite to the case of the ordinary fmp–the absolute majority of important logics have fmp, but not with respect to admissibility. As regards logics of width ≤ 2, there exists a zone for fmp w. r. t. admissibility. It is shown (Theorem 4.3) that all modal logics A of width ≤ 2 extending S4 which are not sub‐logics of three special tabular logics (which is equipotent to all these λ extend a certain subframe logic defined over S4 by omission of four special frames) have fmp w.r.t.

ISSN:0942-5616    

DOI:10.1002/malq.19990450409

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1999

数据来源: WILEY

摘要:

AbstractIn this paper we analyze an extension of Martin‐Löf s intensional set theory by means of a set contructorPsuch that the elements ofP(S) are the subsets of the setS.Since it seems natural to require some kind of extensionality on the equality among subsets, it turns out that such an extension cannot be constructive. In fact we will prove that this extension is classic, that is “(A V ⌝ A)trueholds for any propos

ISSN:0942-5616    

DOI:10.1002/malq.19990450410

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1999

数据来源: WILEY

摘要:

AbstractWe prove that there exists no sentenceFof the language of rings with an extra binary predicat I2satisfying the following property: for every definable setX⊆ ℂ2,Xis connected if and only if (ℂ,X) ⊧F, whereI2is interpreted byX.We conjecture that the same result holds for closed subset of ℂ2. We prove some results motivated by this c

ISSN:0942-5616    

DOI:10.1002/malq.19990450411

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1999

数据来源: WILEY