The logical basis for computer programming. Volume 1: deductive reasoning
The logical basis for computer programming. Volume 1: deductive reasoning
Logic for problem-solving
The logical basis for computer programming: vol. 2, deductive systems
The logical basis for computer programming: vol. 2, deductive systems
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
A Deductive Approach to Program Synthesis
ACM Transactions on Programming Languages and Systems (TOPLAS)
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
Resolution by unification and equality
Resolution by unification and equality
Theory links: Applications to automated theorem proving
Journal of Symbolic Computation
Deductive synthesis of sorting programs
Journal of Symbolic Computation
Note on theorem proving strategies for resolution counterparts of non-classical logics
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Nonclausal deduction in first-order temporal logic
Journal of the ACM (JACM)
Resolution proof systems with weak transformation rules
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Fundamentals of Deductive Program Synthesis
IEEE Transactions on Software Engineering
Constructing specification morphisms
Journal of Symbolic Computation - Special issue on automatic programming
The deductive synthesis of database transactions
ACM Transactions on Database Systems (TODS)
Ordered chaining calculi for first-order theories of transitive relations
Journal of the ACM (JACM)
Polarity guided tractable reasoning
AAAI '99/IAAI '99 Proceedings of the sixteenth national conference on Artificial intelligence and the eleventh Innovative applications of artificial intelligence conference innovative applications of artificial intelligence
Term Rewriting in a Logic of Special Relations
AMAST '98 Proceedings of the 7th International Conference on Algebraic Methodology and Software Technology
Non-Clausal Reasoning with Definite Theories
Fundamenta Informaticae
Rewriting with Equivalence Relations in ACL2
Journal of Automated Reasoning
The origin of the binary-search paradigm
IJCAI'85 Proceedings of the 9th international joint conference on Artificial intelligence - Volume 1
Determination of α-resolution in lattice-valued first-order logic LF(X)
Information Sciences: an International Journal
Non-Clausal Reasoning with Definite Theories
Fundamenta Informaticae
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Two deduction rules are introduced to give streamlined treatment to relations of special importance in an automated theorem-proving system. These rules, the relation replacement and relation matching rules, generalize to an arbitrary binary relation the paramodulation and E-resolution rules, respectively, for equality, and may operate within a nonclausal or clausal system. The new rules depend on an extension of the notion of polarity to apply to subterms as well as to subsentences, with respect to a given binary relation. The rules allow us to eliminate troublesome axioms, such as transitivity and monotonicity, from the system; proofs are shorter and more comprehensible, and the search space is correspondingly deflated.