# Methods and Applications of Mathematical Logic

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*Walter A. Carnielli; Luiz Paulo de Alcantara*

This volume constitutes the proceedings of the Seventh Latin American Symposium on Mathematical Logic, held July 29–August 2, 1985, at the University of Campinas in Brazil. Striking a balance between breadth of scope and depth of results, the papers in this collection range over a variety of topics in classical and non-classical logics. The book provides readers with an introduction to the active lines of research in mathematical logic and particularly emphasizes the connections to other fields, especially philosophy, computer science, and probability theory. The potential applicability of the mathematical methods studied in logic has become important because various areas—such as software engineering, mathematical biology, physics, and linguistics—now appear to need mathematical methods of the kind studied in logic.

# Table of Contents

## Methods and Applications of Mathematical Logic

- Contents vii8 free
- Preface ix10 free
- Introduction xi12 free
- The scientific work of A. I. Arruda 114 free
- Section I – Foundations of set theory 1730
- Section II – Algebraic logic 4356
- Section III – Philosophical aspects of mathematical logic 7790
- Section IV – Interactions between logic, mathematics and computer science 99112
- Logics and pseudogroups 101114
- Sets of relational systems as models for stochastic processes 117130
- A general framework for semantics for propasotional logics 149162
- Formal languages and topological spaces 169182
- Automatic theorem proving: an attempt to improve readability of proofs generated by resolution 179192
- The downward löwenheim-Skolem theorem for L-structures in Ω-sets 189202
- The derivative of truth in Łukasiewicz sentential calculus 209222
- Equivalence relations on lattices and the complexity of the theory of permutations which commute 229242
- Problem solving by interpretation of theories 241254