scholarly journals Topological and Multi-Topological Frames in the Context of Intuitionistic Modal Logic

2019 ◽  
Vol 48 (3) ◽  
pp. 187-205
Author(s):  
Tomasz Witczak
Keyword(s):  
Modal Logic ◽  
Point Of View ◽  
Modal Operator ◽  
Topological Semantics ◽  
Neighborhood Models ◽  
Intuitionistic Modal Logic ◽  
Neighborhood Structures

We present three examples of topological semantics for intuitionistic modal logic with one modal operator □. We show that it is possible to treat neighborhood models, introduced earlier, as topological or multi-topological. From the neighborhood point of view, our method is based on differences between properties of minimal and maximal neighborhoods. Also we propose transformation of multitopological spaces into the neighborhood structures.

QUANTIFIED MODAL LOGIC ON THE RATIONAL LINE

2014 ◽  
Vol 7 (3) ◽  
pp. 439-454 ◽  
Author(s):  
PHILIP KREMER
Keyword(s):  
Modal Logic ◽  
Real Line ◽  
Topological Spaces ◽  
Topological Semantics ◽  
Cantor Space ◽  
Quantified Modal Logic ◽  
Propositional Modal Logic ◽  
The Family ◽  
Modal Logic S4 ◽  
Rational Line

AbstractIn the topological semantics for propositional modal logic, S4 is known to be complete for the class of all topological spaces, for the rational line, for Cantor space, and for the real line. In the topological semantics for quantified modal logic, QS4 is known to be complete for the class of all topological spaces, and for the family of subspaces of the irrational line. The main result of the current paper is that QS4 is complete, indeed strongly complete, for the rational line.

On finite and infinite modal systems

1938 ◽  
Vol 3 (2) ◽  
pp. 77-82 ◽  
Author(s):  
C. West Churchman
Keyword(s):  
Modal Logic ◽  
Symbolic Logic ◽  
Modal Operator ◽  
Image Position ◽  
Modal Systems ◽  
Complex Modal

In Oskar Becker's Zur Logik der Modalitäten four systems of modal logic are considered. Two of these are mentioned in Appendix II of Lewis and Langford's Symbolic logic. The first system is based on A1–8 plus the postulate,From A7: ∼◊p⊰∼p we can prove the converse of C11 by writing ∼◊p for p, and hence deriveThe addition of this postulate to A1–8, as Becker points out, allows us to “reduce” all complex modal functions to six, and these six are precisely those which Lewis mentions in his postulates and theorems: p, ∼p, ◊p, ∼◊p, ∼◊∼p, and ◊∼p This reduction is accomplished by showingwhere ◊n means that the modal operator ◊ is repeated n times; e.g., ◊3p = ◊◊◊p. Then it is shown thatBy means of (1), (2), and (3) any complex modal function whatsoever may be reduced to one of the six “simple” modals mentioned above.It might be asked whether this reduction could be carried out still further, i.e., whether two of the six “irreducible” modals could not be equated. But such a reduction would have to be based on the fact that ◊p = p which is inconsistent with the set B1–9 of Lewis and Langford's Symbolic logic and independent of the set A1–8. Hence for neither set would such a reduction be possible.

scholarly journals Bilinear Assignment Problem: Large Neighborhoods and Experimental Analysis of Algorithms

2020 ◽  
Vol 32 (3) ◽  
pp. 730-746
Author(s):  
Vladyslav Sokol ◽  
Ante Ćustić ◽  
Abraham P. Punnen ◽  
Binay Bhattacharya
Keyword(s):  
Experimental Analysis ◽  
Assignment Problem ◽  
Heuristic Algorithms ◽  
Analysis Of Algorithms ◽  
Quadratic Assignment Problem ◽  
Point Of View ◽  
Neighborhood Search ◽  
Quadratic Assignment ◽  
Neighborhood Structures ◽  
Experimental Analysis Of Algorithms

The bilinear assignment problem (BAP) is a generalization of the well-known quadratic assignment problem. In this paper, we study the problem from the computational analysis point of view. Several classes of neighborhood structures are introduced for the problem along with some theoretical analysis. These neighborhoods are then explored within a local search and variable neighborhood search frameworks with multistart to generate robust heuristic algorithms. In addition, we present several very fast construction heuristics. Our systematic experimental analysis disclosed some interesting properties of the BAP, different from those of comparable models. We have also introduced benchmark test instances that can be used for future experiments on exact and heuristic algorithms for the problem.

scholarly journals Intuitionistic Modal Logic and Applications (IMLA 2008)

2011 ◽  
Vol 209 (12) ◽  
pp. 1435-1436
Author(s):  
Valeria de Paiva ◽  
Brigitte Pientka
Keyword(s):  
Modal Logic ◽  
Intuitionistic Modal Logic

scholarly journals Optimizing Computer Networks Communication with the Band Collocation Problem: A Variable Neighborhood Search Approach

Electronics ◽  
2020 ◽  
Vol 9 (11) ◽  
pp. 1860
Author(s):  
Isaac Lozano-Osorio ◽  
Jesus Sanchez-Oro ◽  
Miguel Ángel Rodriguez-Garcia ◽  
Abraham Duarte
Keyword(s):  
Variable Neighborhood Search ◽  
Simulated Annealing Algorithm ◽  
Previous Method ◽  
Point Of View ◽  
Telecommunication Networks ◽  
Neighborhood Search ◽  
Neighborhood Structures ◽  
Bandpass Problem ◽  
Search Approach ◽  
The Cost

The Band Collocation Problem appears in the context of problems for optimizing telecommunication networks with the aim of solving some concerns related to the original Bandpass Problem and to present a more realistic approximation to be solved. This problem is interesting to optimize the cost of networks with several devices connected, such as networks with several embedded systems transmitting information among them. Despite the real-world applications of this problem, it has been mostly ignored from a heuristic point of view, with the Simulated Annealing algorithm being the best method found in the literature. In this work, three Variable Neighborhood Search (VNS) variants are presented, as well as three neighborhood structures and a novel optimization based on Least Recently Used cache, which allows the algorithm to perform an efficient evaluation of the objective function. The extensive experimental results section shows the superiority of the proposal with respect to the best previous method found in the state-of-the-art, emerging VNS as the most competitive method to deal with the Band Collocation Problem.

scholarly journals A bi-intuitionistic modal logic: Foundations and automation

2016 ◽  
Vol 85 (4) ◽  
pp. 500-519 ◽  
Author(s):  
John G. Stell ◽  
Renate A. Schmidt ◽  
David Rydeheard
Keyword(s):  
Modal Logic ◽  
Intuitionistic Modal Logic

A general treatment of equivalent modalities

1989 ◽  
Vol 54 (4) ◽  
pp. 1460-1471
Author(s):  
Fabio Bellissima ◽  
Massimo Mirolli
Keyword(s):  
Modal Logic ◽  
Minimal Element ◽  
Continuum Hypothesis ◽  
Classical Problem ◽  
Point Of View ◽  
General Treatment ◽  
General Point ◽  
Whole Class ◽  
The Continuum

The problem of the nonequivalent modalities available in certain systems is a classical problem of modal logic. In this paper we deal with this problem without referring to particular logics, but considering the whole class of normal propositional logics. Given a logic L let P(L) (the m-partition generated by L) denote the set of the classes of L-equivalent modalities. Obviously, different logics may generate the same m-partition; the first problem arising from this general point of view is therefore to determine the cardinality of the set of all m-partitions. Since, as is well known, there exist normal logics, and since one immediately realizes that there are infinitely many m-partitions, the problem consists in choosing (assuming the continuum hypothesis) between ℵ0 and . In Theorem 1.2 we show that there are m-partitions, as many as the logics.The next problem which naturally arises consists in determining, given an m-partition P(L), the number of logics generating P(L) (in symbols, μ(P(L))). In Theorem 2.1(ii) we show that ∣{P(L): μ(P(L)) = }∣ = . Now, the set {L′) = P(L)} has a natural minimal element; that is, the logic L* axiomatized by K ∪ {φ(p) ↔ ψ(p): φ, ψ are L-equivalent modalities}; P(L) and L* can be, in some sense, identified, thus making the set of m-partitions a subset of the set of logics.

A proof-theoretic study of the correspondence of classical logic and modal logic

2003 ◽  
Vol 68 (4) ◽  
pp. 1403-1414 ◽  
Author(s):  
H. Kushida ◽  
M. Okada
Keyword(s):  
Modal Logic ◽  
Classical Logic ◽  
Predicate Logic ◽  
Transformation Method ◽  
Modal Operator ◽  
Theoretic Method ◽  
Barcan Formula ◽  
Theoretic Proof ◽  
Classical Predicate

AbstractIt is well known that the modal logic S5 can be embedded in the classical predicate logic by interpreting the modal operator in terms of a quantifier. Wajsberg [10] proved this fact in a syntactic way. Mints [7] extended this result to the quantified version of S5; using a purely proof-theoretic method he showed that the quantified S5 corresponds to the classical predicate logic with one-sorted variable. In this paper we extend Mints' result to the basic modal logic S4; we investigate the correspondence between the quantified versions of S4 (with and without the Barcan formula) and the classical predicate logic (with one-sorted variable). We present a purely proof-theoretic proof-transformation method, reducing an LK-proof of an interpreted formula to a modal proof.

□ In intuitionistic modal logic

1997 ◽  
Vol 75 (2) ◽  
pp. 201-213 ◽  
Author(s):  
David DeVidi ◽  
Graham Solomon
Keyword(s):  
Modal Logic ◽  
Intuitionistic Modal Logic

scholarly journals Logics with Impossibility as the Negation and Regular Extensions of the Deontic Logic D2

2017 ◽  
Vol 46 (3/4) ◽  
Author(s):  
Krystyna Mruczek-Nasieniewska ◽  
Marek Nasieniewski
Keyword(s):  
Intuitionistic Logic ◽  
Deontic Logic ◽  
Modus Ponens ◽  
Modal Logics ◽  
Point Of View ◽  
Modal Operator ◽  
Modal Interpretation ◽  
Semantical Point ◽  
The Right ◽  
Normal Modal Logics

In [1] J.-Y. Bèziau formulated a logic called Z. Bèziau’s idea was generalized independently in [6] and [7]. A family of logics to which Z belongs is denoted in [7] by K. In particular; it has been shown in [6] and [7] that there is a correspondence between normal modal logics and logics from the class K. Similar; but only partial results has been obtained also for regular logics (see [8] and [9]). In (Došen; [2]) a logic N has been investigated in the language with negation; implication; conjunction and disjunction by axioms of positive intuitionistic logic; the right-to-left part of the second de Morgan law; and the rules of modus ponens and contraposition. From the semantical point of view the negation used by Došen is the modal operator of impossibility. It is known this operator is a characteristic of the modal interpretation of intuitionistic negation (see [3; p. 300]). In the present paper we consider an extension of N denoted by N+. We will prove that every extension of N+ that is closed under the same rules as N+; corresponds to a regular logic being an extension of the regular deontic logic D21 (see [4] and [13]). The proved correspondence allows to obtain from soundnesscompleteness result for any given regular logic containing D2, similar adequacy theorem for the respective extension of the logic N+.

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