Title: Intensional FOL for reasoning about probabilities and probabilistic logic programming

Authors: Zoran Majkić; Bhanu Prasad

Addresses: ISRST, Roma, Italy ' Department of Computer and Information Sciences, Florida A&M University, Tallahassee, Florida 32307, USA

Abstract: It is important to have a logic, both for computation of probabilities and for reasoning about probabilities, with well-defined syntax and semantics. The current approaches, which are based on Nilsson's probability structures/logics as well as linear inequalities, to reason about probabilities, have some deficiencies. In this research, we have presented a complete revision of those approaches and have shown that the logic for reasoning about probabilities can be naturally embedded into a 2-valued intensional first-order logic (FOL) with intensional abstraction, by avoiding current ad-hoc system composed of two different 2-valued logics: one for the classical propositional logic at a lower-level and a new one, at a higher-level, for probabilistic constraints with probabilistic variables. The theoretical results that are obtained are applied to probabilistic logic programming.

Keywords: probabilities; 2-valued intensional first-order logic; Nilsson's probability structures; linear inequalities.

DOI: 10.1504/IJIIDS.2018.091627

International Journal of Intelligent Information and Database Systems, 2018 Vol.11 No.1, pp.79 - 96

Received: 17 Nov 2017
Accepted: 30 Nov 2017
Published online: 08 May 2018 *

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