Formalization of the Resolution Calculus for First-Order Logic
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DOI: 10.1007/s10817-017-9447-z
Abstract: I present a formalization in Isabelle/HOL of the resolution calculus for first-order logic with formal soundness and completeness proofs. To prove the calculus sound, I use the substitution lemma, and to prove it complete, I… read more here.
Keywords: resolution; first order; calculus; order logic ... See more keywords
An analysis of Existential Graphs–part 2: Beta
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DOI: 10.1007/s11229-021-03134-3
Abstract: This paper provides an analysis of the notational difference between Beta Existential Graphs, the graphical notation for quantificational logic invented by Charles S. Peirce at the end of the 19th century, and the ordinary notation of first-order… read more here.
Keywords: notation; existential graphs; beta; first order ... See more keywords
Approximation Fixpoint Theory and the Well-Founded Semantics of Higher-Order Logic Programs
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DOI: 10.1017/s1471068418000108
Abstract: Abstract We define a novel, extensional, three-valued semantics for higher-order logic programs with negation. The new semantics is based on interpreting the types of the source language as three-valued Fitting-monotonic functions at all levels of… read more here.
Keywords: higher order; semantics higher; logic programs; order logic ... See more keywords
CSE_E 1.0: An Integrated Automated Theorem Prover for First-Order Logic
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DOI: 10.3390/sym11091142
Abstract: First-order logic is an important part of mathematical logic, and automated theorem proving is an interdisciplinary field of mathematics and computer science. The paper presents an automated theorem prover for first-order logic, called C S… read more here.
Keywords: automated theorem; order; first order; cse ... See more keywords