A formalization in Isabelle/HOL of the resolution calculus for first-order logic with formal soundness and completeness proofs and a thorough overview of formalizations of first- order logic found in the literature is given.Expand

A new software tool for teaching logic based on natural deduction that is developed for undergraduate computer science students who are used to study and program concrete computer code in a programming language and for other proof systems as well.Expand

We present an Isabelle/HOL formalization of the first half of Bachmair and Ganzinger’s chapter on resolution theorem proving, culminating with a refutationally complete first-order prover based on… Expand

This work specifies, using Isabelle/HOL, a purely functional first-order ordered resolution prover and establishes its soundness and refutational completeness, and applies stepwise refinement to obtain, from an abstract nondeterministic specification, a verified deterministic program.Expand

It is demonstrated that SSI concepts can be integrated into TPL without changing the syntax and semantics of TPL itself and have to add new formats and introduce a new built-in predicate for interacting with the DL.Expand

We present a certified declarative first-order prover with equality based on John Harrison’s Handbook of Practical Logic and Automated Reasoning, Cambridge University Press, 2009. ML code reflection… Expand

This theory is a formalization of the resolution calculus for firstorder logic which employs Herbrand’s theorem in a formulation which states that an unsatisfiable set of clauses has a finite closed semantic tree and is proven sound and complete.Expand

In Isabelle/HOL the kernel of an LCF-style prover for first-order logic with equality from John Harrison’s Handbook of Practical Logic and Automated Reasoning is formalized and the kernel sound is proved and Standard ML code is generated from the formalization.Expand

It is shown how to use the proof assistant Isabelle to formally prove theorems in the logic as well as meta-theorems about the logic, which has a countably infinite number of non-classical truth values.Expand

This paper formalizes the substitutionless proof system in Isabelle/HOL, spelling out its side conditions explicitly and verifying its soundness, and shows that this formulation is equivalent in expressive power to ordinary first-order logic.Expand