Abstract

MARTINEZ, Iveth  and  PIZA, Eduardo. Decision problems and recursiveness in formal logic systems. Rev. Mat [online]. 2016, vol.23, n.1, pp.11-39. ISSN 1409-2433.

The recursion theory states that a decision problem is recursively solvable if there is a mechanical process to solve it. Within the context of formal logic, the decision problem consist to determine whether any wellformed formula of the system is a theorem or not.

This paper first discusses, among other things, the famous problem of decision of the canonical first-order logic F0 (also called Entscheidungsproblem) from a modern perspective. Then we study the decision problem of the partial propositional logics. It exploits the development achieved by recursion theory and semi-Thue production systems after the work of Post and Kleene in the 40's and Davis in the early 70's, among others, to explain a solution to these decision problems.

Keywords : decision problems; formal logic; first-order logic; Entscheidungsproblem; partial propositional logics; semi-Thue production systems.

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