scholarly journals REFLEXIVE-INSENSITIVE MODAL LOGICS

2015 ◽  
Vol 9 (1) ◽  
pp. 167-180 ◽  
Author(s):  
DAVID R. GILBERT ◽  
GIORGIO VENTURI
Keyword(s):  
Completeness Theorem ◽  
Modal Logics ◽  
Modal Operator ◽  
Semantic Condition ◽  
Definition Of ◽  
Normal Modal Logics ◽  
Semantic Definition

AbstractWe analyze a class of modal logics rendered insensitive to reflexivity by way of a modification to the semantic definition of the modal operator. We explore the extent to which these logics can be characterized, and prove a general completeness theorem on the basis of a translation between normal modal logics and their reflexive-insensitive counterparts. Lastly, we provide a sufficient semantic condition describing when a similarly general soundness result is also available.

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+.

scholarly journals Synthesizing Normal and Non-Normal Modal Logics in Philosophical Epistemology Axiomatic System Modeled by the Logic Square and Hexagon of Opposition

2019 ◽  
pp. 894-907
Author(s):  
Vladimir O. Lobovikov
Keyword(s):  
Axiom System ◽  
Difficult Problem ◽  
Modal Logics ◽  
Axiomatic System ◽  
Border Line ◽  
History Of ◽  
The One ◽  
Definition Of ◽  
Axiomatic Systems ◽  
Normal Modal Logics

The paper aims at coping with the difficult problem of rationally uniting astonishingly huge amount of qualitatively different modal logics. For realizing this aim artificial languages of symbolic logic and the axiomatic methodology are used. Therefore, the method of constructing and studying formal logic inferences within the axiom system under investigation is exploited systematically. Inventing and elaborating a hitherto not-considered axiomatic system of epistemology uniting normal and not-normal modal logics is the new nontrivial scientific result of this work. History of philosophy and systematical philosophy, formal ethics and formal aesthetics, philosophical epistemology and analytical theology, philosophy of law and philosophy of science are among the important fields of application of the nontrivial abstract-theoretic principles demonstrated in this paper. Using the above-indicated machinery the author has arrived to the following main conclusion: the famous philosophical principles of utilitarianism, hedonism, optimism, pragmatism, fideism, falsifiability, verifiability, “Hume’s Guillotine”, “naturalistic fallacies” et al have not absolutely indefinite (unlimited) but quite definite (limited) sphere of relevant applicability; the precise formal definition of the border-line of mentioned sphere of relevance is the axiomatic one submitted and discussed in the paper. This general conclusion is instantiated in the text by several particular conclusions concerning explication and clarification of specific philosophical ideas and principles, for example, the one of kalokagathia. The author concludes that constructing and investigating the axiomatic systems of universal philosophical epistemology is indispensable for adequate representing human knowledge in artificial intellectual systems, for instance, in autonomous AI‑robots

A formal semantic definition of DEVIL

2003 ◽  
Vol 38 (4) ◽  
pp. 47-56 ◽  
Author(s):  
Lei Luo ◽  
Ming-Yuan Zhu ◽  
Qing-Li Zhang
Keyword(s):  
Formal Semantic ◽  
Definition Of ◽  
Semantic Definition

Experience with the formal semantic definition of HAL/S

1982 ◽  
Vol 17 (6) ◽  
pp. 327-333
Author(s):  
Terrence W. Pratt ◽  
George D. Maydwell
Keyword(s):  
Formal Semantic ◽  
Definition Of ◽  
Semantic Definition

On The Semantic Definition of Truth

1963 ◽  
Vol 2 (1-2) ◽  
pp. 96-101
Author(s):  
P. V. Tavanets
Keyword(s):  
Definition Of ◽  
Semantic Definition

scholarly journals Control Flow Treatment in a Simple: Semantics-Directed Compiler Generator

1981 ◽  
Vol 10 (137) ◽  
Author(s):  
Neil D. Jones ◽  
Henning Christiansen
Keyword(s):  
Simple Algebra ◽  
Control Flow ◽  
Program Execution ◽  
Correctness Proofs ◽  
Compiler Generation ◽  
Source Program ◽  
Target Program ◽  
Definition Of ◽  
Flow Treatment ◽  
Semantic Definition

<p>A simple algebra-based algorithm for compiler generation is described. Its input is a semantic definition of a programming language, and its output is a ''compiling semantics'' which maps each source program into a sequence of compile-time actions whose net effect on execution is the production of a semantically equivalent target program. The method does not require individual compiler correctness proofs or the construction of specialized target algebras.</p><p>Source program execution is assumed to proceed by performing a series of elementary actions on a runtime state. A semantic algebra is introduced to represent and manipulate possible execution sequences. A source semantic definition has two parts: A set of semantic equations mapping source programs into terms of the algebra, and an interpretation which gives concrete definitions of the state and the elementary actions on it.</p>

scholarly journals Fusions of Description Logics and Abstract Description Systems

2002 ◽  
Vol 16 ◽  
pp. 1-58 ◽  
Author(s):  
F. Baader ◽  
C. Lutz ◽  
H. Sturm ◽  
F. Wolter
Keyword(s):  
Large Class ◽  
Description Logics ◽  
General Setting ◽  
Modal Logics ◽  
Common Generalization ◽  
Abstract Description ◽  
Normal Modal Logics ◽  
Combining Logics

Fusions are a simple way of combining logics. For normal modal logics, fusions have been investigated in detail. In particular, it is known that, under certain conditions, decidability transfers from the component logics to their fusion. Though description logics are closely related to modal logics, they are not necessarily normal. In addition, ABox reasoning in description logics is not covered by the results from modal logics. In this paper, we extend the decidability transfer results from normal modal logics to a large class of description logics. To cover different description logics in a uniform way, we introduce abstract description systems, which can be seen as a common generalization of description and modal logics, and show the transfer results in this general setting.

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