Update Semantics in Communicated Information System

2011 ◽  
Vol 403-408 ◽  
pp. 1460-1465
Author(s):  
Guang Ming Chen ◽  
Xiao Wu Li
Keyword(s):  
Information Systems ◽  
Propositional Logic ◽  
General Purpose ◽  
Main Task ◽  
Information Communication ◽  
Classical Propositional Logic ◽  
Update Semantics ◽  
Essential Form ◽  
Soundness And Completeness ◽  
Multi Agents

An approach, which is called Communicated Information Systems, is introduced to describe the information available in a number of agents and specify the information communication among the agents. The systems are extensions of classical propositional logic in multi-agents context, providing with us a way by which not only the agent’s own information, but the information from other agents may be applied to agent’s reasoning as well. Communication rules, which are defined in the most essential form, can be regarded as the base to characterize some interesting cognitive proporties of agents. Since the corresponding communication rules can be chosen for different applications, the approach is general purpose one. The other main task is that the soundness and completeness of the Communicated Information Systems for the update semantics have been proved in the paper.

scholarly journals Deduction in Non-Fregean Propositional Logic SCI

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 115 ◽  
Author(s):  
Joanna Golińska-Pilarek ◽  
Magdalena Welle
Keyword(s):  
Propositional Logic ◽  
Sequent Calculus ◽  
Classical Propositional Logic ◽  
Tableau System ◽  
Soundness And Completeness

We study deduction systems for the weakest, extensional and two-valued non-Fregean propositional logic SCI . The language of SCI is obtained by expanding the language of classical propositional logic with a new binary connective ≡ that expresses the identity of two statements; that is, it connects two statements and forms a new one, which is true whenever the semantic correlates of the arguments are the same. On the formal side, SCI is an extension of classical propositional logic with axioms characterizing the identity connective, postulating that identity must be an equivalence and obey an extensionality principle. First, we present and discuss two types of systems for SCI known from the literature, namely sequent calculus and a dual tableau-like system. Then, we present a new dual tableau system for SCI and prove its soundness and completeness. Finally, we discuss and compare the systems presented in the paper.

scholarly journals Hybrid Deduction–Refutation Systems

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 118 ◽  
Author(s):  
Valentin Goranko
Keyword(s):  
Propositional Logic ◽  
Proof Theory ◽  
Natural Deduction ◽  
Basic Theory ◽  
Logical System ◽  
Classical Propositional Logic ◽  
Deductive Systems ◽  
Refutation Systems ◽  
Soundness And Completeness

Hybrid deduction–refutation systems are deductive systems intended to derive both valid and non-valid, i.e., semantically refutable, formulae of a given logical system, by employing together separate derivability operators for each of these and combining ‘hybrid derivation rules’ that involve both deduction and refutation. The goal of this paper is to develop a basic theory and ‘meta-proof’ theory of hybrid deduction–refutation systems. I then illustrate the concept on a hybrid derivation system of natural deduction for classical propositional logic, for which I show soundness and completeness for both deductions and refutations.

scholarly journals Logics for Knowability

2021 ◽  
pp. 1-42
Author(s):  
Mo Liu ◽  
Jie Fan ◽  
Hans Van Ditmarsch ◽  
Louwe B. Kuijer
Keyword(s):  
Propositional Logic ◽  
Single Agent ◽  
Classical Propositional Logic ◽  
Public Announcement ◽  
Public Announcement Logic ◽  
Multi Agent ◽  
Soundness And Completeness

In this paper, we propose three knowability logics LK, LK−, and LK=. In the single-agent case, LK is equally expressive as arbitrary public announcement logic APAL and public announcement logic PAL, whereas in the multi-agent case, LK is more expressive than PAL. In contrast, both LK− and LK= are equally expressive as classical propositional logic PL. We present the axiomatizations of the three knowability logics and show their soundness and completeness. We show that all three knowability logics possess the properties of Church-Rosser and McKinsey. Although LK is undecidable when at least three agents are involved, LK− and LK= are both decidable.

RELEVANCE LOGIC AND THE CALCULUS OF RELATIONS

2010 ◽  
Vol 3 (1) ◽  
pp. 41-70 ◽  
Author(s):  
ROGER D. MADDUX
Keyword(s):  
Propositional Logic ◽  
Relevance Logic ◽  
Binary Relations ◽  
Classical Propositional Logic

Sound and complete semantics for classical propositional logic can be obtained by interpreting sentences as sets. Replacing sets with commuting dense binary relations produces an interpretation that turns out to be sound but not complete for R. Adding transitivity yields sound and complete semantics for RM, because all normal Sugihara matrices are representable as algebras of binary relations.

scholarly journals The Method of Socratic Proofs Meets Correspondence Analysis

2019 ◽  
Vol 48 (2) ◽  
pp. 99-116
Author(s):  
Dorota Leszczyńska-Jasion ◽  
Yaroslav Petrukhin ◽  
Vasilyi Shangin
Keyword(s):  
Correspondence Analysis ◽  
Boolean Functions ◽  
Propositional Logic ◽  
Sequent Calculus ◽  
Sequent Calculi ◽  
Classical Propositional Logic ◽  
Logic Of Questions ◽  
Proof Systems

The goal of this paper is to propose correspondence analysis as a technique for generating the so-called erotetic (i.e. pertaining to the logic of questions) calculi which constitute the method of Socratic proofs by Andrzej Wiśniewski. As we explain in the paper, in order to successfully design an erotetic calculus one needs invertible sequent-calculus-style rules. For this reason, the proposed correspondence analysis resulting in invertible rules can constitute a new foundation for the method of Socratic proofs. Correspondence analysis is Kooi and Tamminga's technique for designing proof systems. In this paper it is used to consider sequent calculi with non-branching (the only exception being the rule of cut), invertible rules for the negation fragment of classical propositional logic and its extensions by binary Boolean functions.

SUSPENSION CIVIL PROTECTION UNIT IN KOSOVO AND METOHIJA

2021 ◽  
pp. 277-289
Author(s):  
VLADIMIR JAKOVLJEVIĆ ◽  
MILOŠ TOMIĆ
Keyword(s):  
Local Population ◽  
Institutional Arrangement ◽  
General Purpose ◽  
National Minority ◽  
Main Task ◽  
Civil Protection ◽  
The North ◽  
Rescue System ◽  
The Republic

The gradual suspension of the institutions of the Republic of Serbia in the area of Kosovo and Metohija is the result of the dialogue that the representatives of the Albanian national minority are having with the Serbian political leadership. The first agreement, signed in 2013, formally and legally calls into question the survival and functioning of a number of institutions that function in accordance with the legislation of the RS and are of vital importance for the security of the local population. As an important part of the institutional arrangement and organization of the protection and rescue system, civil protection units were formed within four municipalities in the north of Kosmet, as well as in other parts south of the river Ibar. The main task of the trained and trained general purpose units was to protect people, material and cultural goods and the environment from natural disasters and technical-technological accidents. However, a section of the international community, along with Albanian political leaders, views the unit as a "paramilitary organization" (despite their humanitarian character), demanding their immediate disbandment and involvement in Kosovo's provisional institutions. The aim of this paper is a systematic description and analysis of the current security situation in the southern Serbian province as well as the role of civil protection units in maintaining a stable security situation. The paper uses the method of content analysis of a number of relevant documents describing the attempt to include members of civil protection units in the work of Kosovo's provisional institutions.

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