Equational logic as a programming language
Equational logic as a programming language
Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
Some results and experiments in programming techniques for propositional logic
Computers and Operations Research - Special issue: Applications of integer programming
Introduction to mathematical logic (3rd ed.)
Introduction to mathematical logic (3rd ed.)
An introduction to mathematical logic and type theory: to truth through proof
An introduction to mathematical logic and type theory: to truth through proof
Empirical explorations with the logic theory machine: a case study in heuristics
Computers & thought
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
A Proof Procedure Using Connection Graphs
Journal of the ACM (JACM)
Fast Decision Procedures Based on Congruence Closure
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Logic for Problem Solving
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
On proving inductive properties of abstract data types
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Automated Reasoning: Introduction and Applications
Automated Reasoning: Introduction and Applications
How to Prove Algebraic Inductive Hypotheses Without Induction
Proceedings of the 5th Conference on Automated Deduction
Deciding Combinations of Theories
Proceedings of the 6th Conference on Automated Deduction
Logic Machine Architecture: Kernel Funtions
Proceedings of the 6th Conference on Automated Deduction
Expansion Tree Proofs and Their Conversion to Natural Deduction Proofs
Proceedings of the 7th International Conference on Automated Deduction
Proceedings of the 7th International Conference on Automated Deduction
Automated theorem proving: A logical basis (Fundamental studies in computer science)
Automated theorem proving: A logical basis (Fundamental studies in computer science)
Goal-Directed Context Validation for Adaptive Ubiquitous Systems
SEAMS '07 Proceedings of the 2007 International Workshop on Software Engineering for Adaptive and Self-Managing Systems
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Logic can be defined as the formal study of reasoning; if we replace “formal” by “mechanical” we can place almost the entire set of methodologies used in the field of automated theorem proving (ATP) within the scope of logic. Because of the goals of ATP, if not always the methodologies, ATP has been considered to be within the domain of AI. We explore the methodologies of ATP, including the logics that underlie the theorem provers, and discuss some of the mechanisms that utilize these logics. These include term rewriting systems, mathematical induction, inductionless induction and even mixed integer programming. The ATP field, via resolution, has even provided the foundation for an exciting AI and database programming language, PROLOG. We conclude with a new method for extending the PROLOG system to work with non-Horn clause sets within a positive logic format, particularly simple for “slightly non-Horn” clause sets.