How true it is = who says it's true
type: Item
instance of: scholarly article
title: How true it is = who says it's true
zbMATH Open document ID: 1173.03012
author: Melvin Fitting
published in: Studia Logica
publication date: 2009-05-08T00:00:00Z
review text: In this chiefly expository paper the author presents the idea of taking the truth value of a formula to be the set of agents who accept the formula as true. This leads to a truth value space as an arbitrary (finite) Boolean algebra. This is formalized and a complete tableau system provided for a modal logic with propositional constants. This way of looking at things has utility especially for knowledge representation for multiple agents. This is illustrated through discussion of the `muddy children problem'. Nevertheless, as the case study shows, open problems remain regarding the proper formalization of various natural language statements, such as express negative knowledge and common knowledge. The ideas presented here are developed more fully and technically in other works by the author, and others; cf. e.g. [\textit{M. Fitting}, Ann. Soc. Math. Pol., Ser. IV, Fundam. Inf. 15, No.~3--4, 235--254 (1991; Zbl 0745.03018)], [\textit{M. Fitting}, Ann. Soc. Math. Pol., Ser. IV, Fundam. Inf. 17, No.~1--2, 55--73 (1992; Zbl 0772.03006)], [\textit{M. Fitting}, Stud. Log. 55, No.~1, 63--87 (1995; Zbl 0837.03017)].
reviewed by: Louis F. Goble
Mathematics Subject Classification ID: 03B42
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03B50
Mathematics Subject Classification ID: 03A05
zbMATH DE Number: 5552255
zbMATH Keywords: modal logic
zbMATH Keywords: many-valued logic
zbMATH Keywords: logic of knowledge
zbMATH Keywords: Boolean algebra
zbMATH Keywords: bisimulation
zbMATH Keywords: tableau
zbMATH Keywords: truth value
MaRDI profile type: Publication
full work available at URL: s11225-009-9178-1
OpenAlex ID: W2049804170
cites work: Q3858244
cites work: Modal logic
cites work: Notions of bisimulation for Heyting-valued modal languages
cites work: Q3989936
cites work: Q4022223
cites work: Q2757807
cites work: Tableaus for many-valued modal logic
cites work: Q3996619
cites work: Q5465438
cites work: Q3604278
cites work: Bilattices and Modal Operators
cites work: A Catalog ofWeak Many-Valued Modal Axioms and their Corresponding Frame Classes
cites work: Q4458495
cites work: Q3647307
cites work: Q4779594
cites work: Many-valued reflexive autoepistemic logic
cites work: Q5560258
DOI: 10.1007/S11225-009-9178-1
description: scientific article; zbMATH DE number 5552255