ABSTRACT A computational logic, PLPR (Predicate Logic using Polymorphism and Recursion) is presented. Actually this logic is the object language of an automated deduction system designed as a tool for proving mathematical theorems as well as specify and verify properties of functional programs. A useful denotationl semantics and two general deduction methods for PLPR are defined. The first one is a tableau algorithm proved to be complete and also used as a guideline for building complete calculi. The second is a (...) sound and complete natural deduction system. Moreover a fixed point induction rule is introduced for formulas called continuous. The strategies for mechanizing the proofs of the final automated system are based on the previous deduction methods. As the examples of the use of the system show, the implemented theorem prover outperforms humans to a certain extent, retaining logic and calculi generality. (shrink)

The formalization of the languages of mathematics has led to the formal languages of computer science and artificial intelligence. This article studies a few semantic properties of the formal languages of artificial intelligence, which I call languages of sign. This paper compares and opposes the semantic properties of these formal languages of artificial intelligence with the richer semantic properties of the languages of metaphysics and religious faith, which I call languages of symbol.