Minimal temporal epistemic logic
type: Item
instance of: scholarly article
title: Minimal temporal epistemic logic
zbMATH Open document ID: 0866.03014
author: Joeri Engelfriet
published in: Notre Dame Journal of Formal Logic
publication date: 1997-06-26T00:00:00Z
review text: The dynamics of (nonmonotonic) reasoning processes is studied. The presented approach is based on two components: Epistemic logic is used as a formalization of information states. Temporal logic is used as a formalization of a dynamics of information states. A minimal entailment construction (in the style of Shoham) is used in order, to introduce nonmonotonicity into this framework. Some basic assumptions are accepted: Reasoning is conservative, this means, the agent's knowledge increases as he is reasoning. A discrete and linear time is assumed. A temporal epistemic logic (TEL) is the basis of the framework. The epistemic language with the usual S5-semantics is introduced. Pairs \((M,m)\), where \(M\) is a normal S5-model and \(m\in M\) (inuitively, \(m\) is the current world) are called epistemic states. The epistemic language is extended by introducing temporal operators. Semantics of TEL is defined by a function from natural numbers to epistemic states, called TEL-model. Truth of a formula in a TEL-model is defined as it is usual in a temporal semantics (the basic case is truth in S5, for formulae of the epistemic language). An axiomatization of TEL is proposed. Soundness, completeness, and decidability of the system are proven. The interaction between the epistemic part and the temporal part of the logic is quite limited (by the conservativity assumption). The conservativity of the reasoning is formalized as follows. The degree-of-information ordering \(\leq\) on epistemic states is defined. A TEL model \({\mathcal M}\) is called conservative if for each natural number \(s\), \({\mathcal M}(s) \leq {\mathcal M} (s+1)\). Validity and semantical consequence restricted to the class of conservative models (TELC-models), denoted by \(\models^C\), is considered. A sound, complete, and decidable axiomatization of TELC is studied. Minimal conservative models and minimal entailment are studied over TELC. As an example it is shown that minimal entailment can capture skep…
Mathematics Subject Classification ID: 03B60
Mathematics Subject Classification ID: 68T27
Mathematics Subject Classification ID: 03B45
zbMATH DE Number: 944259
zbMATH Keywords: dynamics of nonmonotonic reasoning
zbMATH Keywords: conservativity of reasoning
zbMATH Keywords: degree-of-information ordering on epistemic states
zbMATH Keywords: formalization of information states
zbMATH Keywords: temporal epistemic logic
zbMATH Keywords: temporal semantics
zbMATH Keywords: axiomatization
zbMATH Keywords: minimal entailment
zbMATH Keywords: complexity
zbMATH Keywords: downward persistent formulas
reviewed by: Jan Šefránek
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1040046088
OpenAlex ID: W2023870985
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DOI: 10.1305/NDJFL/1040046088
description: scientific article; zbMATH DE number 944259