## Notre Dame Journal of Formal Logic

- Notre Dame J. Formal Logic
- Volume 37, Number 2 (1996), 233-259.

### Minimal Temporal Epistemic Logic

#### Abstract

In the study of nonmonotonic reasoning the main emphasis has been on static (declarative) aspects. Only recently has there been interest in the dynamic aspects of reasoning processes, particularly in artificial intelligence. We study the dynamics of reasoning processes by using a temporal logic to specify them and to reason about their properties, just as is common in theoretical computer science. This logic is composed of a base temporal epistemic logic with a preference relation on models, and an associated nonmonotonic inference relation, in the style of Shoham, to account for the nonmonotonicity. We present an axiomatic proof system for the base logic and study decidability and complexity for both the base logic and the nonmonotonic inference relation based on it. Then we look at an interesting class of formulas, prove a representation result for it, and provide a link with the rule of monotonicity.

#### Article information

**Source**

Notre Dame J. Formal Logic, Volume 37, Number 2 (1996), 233-259.

**Dates**

First available in Project Euclid: 16 December 2002

**Permanent link to this document**

https://projecteuclid.org/euclid.ndjfl/1040046088

**Digital Object Identifier**

doi:10.1305/ndjfl/1040046088

**Mathematical Reviews number (MathSciNet)**

MR1403819

**Zentralblatt MATH identifier**

0866.03014

**Subjects**

Primary: 03B60: Other nonclassical logic

Secondary: 68T27: Logic in artificial intelligence

#### Citation

Engelfriet, Joeri. Minimal Temporal Epistemic Logic. Notre Dame J. Formal Logic 37 (1996), no. 2, 233--259. doi:10.1305/ndjfl/1040046088. https://projecteuclid.org/euclid.ndjfl/1040046088