Wyniki wyszukiwania - Biblioteka Nauki

1

Modal Equivalence and Bisimilarity in Many-valued Modal Logics with Many-valued Accessibility Relations

100%

Diaconescu D.

Fundamenta Informaticae

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2020

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tom Vol. 173, nr 2-3

177--189

EN

In this paper we investigate the Hennessy-Milner property for models of many-valued modal logics defined based on complete MTL-chains having many-valued accessibility relations. Our main result gives a necessary and sufficient algebraic condition for the class of image-finite models for such modal logics to admit the Hennessy-Milner property.

2

Inconsistency-adaptive modal logics. On how to cope with modal inconsistency

100%

Lycke H.

Logic and Logical Philosophy

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2010

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tom 19

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nr 1-2

31–61

EN

In this paper, I will characterize a new class of inconsistency-adaptive logics, namely inconsistency-adaptive modal logics. These logics cope with inconsistencies in a modal context. More specifically, when faced with inconsistencies, inconsistency-adaptive modal logics avoid explosion, but still allow the derivation of sufficient consequences to adequately explicate the part of human reasoning they are intended for.

3

Admissibility of Cut in Congruent Modal Logics

100%

Indrzejczak A.

Logic and Logical Philosophy

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2011

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tom 20

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nr 3

189-203

EN

We present a detailed proof of the admissibility of cut in sequent calculus for some congruent modal logics. The result was announced much earlier during the Trends in Logic Conference, Toruń 2006 and the proof for monotonic modal logics was provided already in Indrzejczak [5]. Also some tableau and natural deduction formalizations presented in Indrzejczak [6] and Indrzejczak [7] were based on this result but the proof itself was not published so far. In this paper we are going to fill this gap. The delay was partly due to the fact that the author from time to time was trying to improve the result and extend it to some additional logics by testing other methods of proving cut elimination. Unfortunately all these attempts failed and cut elimination holds only for these logics which were proved to satisfy this property already in 2005.

4

Counterpart Semantics for a Second-Order μ-Calculus

100%

Gadducci F. , Lafuente A. L. , Vandin A.

Fundamenta Informaticae

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2012

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tom Vol. 118, nr 1-2

177-205

EN

Quantified &mi;-calculi combine the fix-point and modal operators of temporal logics with (existential and universal) quantifiers, and they allow for reasoning about the possible behaviour of individual components within a software system. In this paper we introduce a novel approach to the semantics of such calculi: we consider a sort of labeled transition systems called counterpart models as semantic domain, where states are algebras and transitions are defined by counterpart relations (a family of partial homomorphisms) between states. Then, formulae are interpreted over sets of state assignments (families of partial substitutions, associating formula variables to state components). Our proposal allows us to model and reason about the creation and deletion of components, as well as the merging of components. Moreover, it avoids the limitations of existing approaches, usually enforcing restrictions of the transition relation: the resulting semantics is a streamlined and intuitively appealing one, yet it is general enough to cover most of the alternative proposals we are aware of. The paper is rounded up with some considerations about expressiveness and decidability aspects.

5

Separability, Expressiveness, and Decidability in the Ambient Logic

88%

Hirschkoff D.

Schedae Informaticae

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2003

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tom Vol. 12

77-84

EN

The Ambient Logic (AL) has been proposed for expressing properties of process mobility in the calculus of Mobile Ambients (MA), and as a basis for query languages on semistructured data. We study some basic questions concerning the descriptive and discriminating power of AL, focusing on the equivalence on processes induced by the logic (= L ). We consider MA, and two Turing complete subsets of it, MA IF and MA synIF , respectively defined by imposing a semantic and a syntactic constraint on process prefixes. The main contributions include: coinductive and inductive operational characterisations of = L on MA synIF; an axiomatisation of = L on MA IF ; the construction of characteristic formulas for the processes in with respect to = L; the decidability of = L on MA IF and on MAsynIF , and its undecidability on MA.

6

Decision procedures for some strong hybrid logics

75%

Indrzejczak A. , Zawidzki M.

Logic and Logical Philosophy

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2013

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tom 22

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nr 4

389-409

EN

Hybrid logics are extensions of standard modal logics, which significantly increase the expressive power of the latter. Since most of hybrid logics are known to be decidable, decision procedures for them is a widely investigated field of research. So far, several tableau calculi for hybrid logics have been presented in the literature. In this paper we introduce a sound, complete and terminating tableau calculus TH(@,E,D,♦ −) for hybrid logics with the satisfaction operators, the universal modality, the difference modality and the inverse modality as well as the corresponding sequent calculus SH(@,E,D,♦ −). They not only uniformly cover relatively wide range of various hybrid logics but they are also conceptually simple and enable effective search for a minimal model for a satisfiable formula. The main novelty is the exploitation of the unrestricted blocking mechanism introduced as an explicit, sound tableau rule.

7

Logika racjonalności. W stronę modalnego platonizmu matematycznego

63%

Wilczek P.

Zagadnienia Filozoficzne w Nauce

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2011

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nr 49

98-122

PL

In this article Whitehead’s philosophy of mathematics is characterized as a Structural Second-Order Platonism and it is demonstrated that the Whiteheadian ontology is consistent with modern formal approaches to the foundation of mathematics. We follow the pathway taken by model-theoretically and semantically oriented philosophers. Consequently, it is supposed that all mathematical theories (understood as deductively closed set of sentences) determine their own models. These models exist mind-independently in the realm of eternal objects. From the metatheoretical point of view the hypothesis (posed by Józef Życiński) of the Rationality Field is explored. It is indicated that relationships between different models can be described in the language of modal logics and can further be axiomatized in the framework of the Second Order Set Theory. In conclusion, it is asserted that if any model (of a mathematical theory) is understood, in agreement with Whitehead’s philosophy, as a collection of eternal objects, which can be simultaneously realized in a single actual occasion, then our external world is governed by the hidden pattern encoded in the field of pure potentialities which constitute the above mentioned Field of Rationality. Therefore, this work can be regarded as the first step towards building a Logic of Rationality.

8

Modal Boolean Connexive Logics: Semantics and Tableau Approach

63%

Jarmużek T. , Malinowski J.

Bulletin of the Section of Logic

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2019

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tom 48

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nr 3

213-243

EN

In this paper we investigate Boolean connexive logics in a language with modal operators: □, ◊. In such logics, negation, conjunction, and disjunction behave in a classical, Boolean way. Only implication is non-classical. We construct these logics by mixing relating semantics with possible worlds. This way, we obtain connexive counterparts of basic normal modal logics. However, most of their traditional axioms formulated in terms of modalities and implication do not hold anymore without additional constraints, since our implication is weaker than the material one. In the final section, we present a tableau approach to the discussed modal logics.

9

On classical behavior of intuitionistic modalities

63%

Drobyshevich S.

Logic and Logical Philosophy

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2015

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tom 24

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nr 1

79–104

EN

We study connections between four types of modal operators – necessity, possibility, un-necessity and impossibility – over intuitionitstic logic in terms of compositions of these modal operators with intuitionistic negation. We investigate which basic compositions, i.e. compositions of the form ¬δ, δ¬ or ¬δ¬, yield modal operators of the same type over intuitionistic logic as over classical logic. We say that such compositions behave classically. We study which modal properties correspond to each basic compositions behaving classically over intuitionistic logic and also prove that KC constitutes the smallest superintuitionistic logic over which all basic compositions behave classically.