Automated Reasoning

This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book

Formalising Overlap Algebras in Matita

We describe some formal topological results, formalized in Matita 1/2, presented in predicative intuitionistic logic and in terms of Overlap Algebras. Overlap Algebras are new algebraic structures designed to ease reasoning about subsets in an algebraic way within intuitionistic logic. We find that they also ease the formalization of formal topological results in an interactive theorem prover. Our main result is the existence of a functor between two categories of ‘generalized topological spaces’, one with points (Basic Pairs) and the other point-free (Basic Topologies). The reported formalization is part as a wider scientific collaboration with the inventor of the theory, Giovanni Sambin. His goal is to verify in what sense, and with what difficulties, his theory is ‘implementable’. We check that all intermediate constructions respect the stringent size requirements imposed by predicative logic. The formalization is quite unusual, since it has to make explicit size information that is often hidden. We found that the version of Matita used for the formalization was largely inappropriate. The formalization drove several major improvements of Matita that will be integrated in the next major release (Matita 1.0). We show some motivating examples for these improvements, taken directly from the formalization. We also describe a possibly sub-optimal solution in Matita 1/2, exploitable in other similar systems. We briefly discuss a better solution available in Matita 1.0