automation for an impoverished logic, and others that feature expressive logics but only limited automation. PVS attempts to tread the middle ground between these two classes by providing mechanical assistance to support clear and abstract specifications, and readable yet sound proofs for difficult theorems

. Isabelle is now based on higher-order logic --- a precise and well-understood foundation. Examples illustrate use of this meta-logic to formalize logics and proofs. Axioms for first-order logic are shown sound and complete. Backwards proof is formalized by meta-reasoning about object-level entailment

First-order unification algorithms (Robinson, 1965) are traditionally implemented via general recursion, with separate proofs for partial correctness and termination. The latter tends to involve counting the number of unsolved variables and showing that this total decreases each time a substitution

This work presents a formalization of the theorem of existence of most general unifiers in first-order signatures in the higher-order proof assistant PVS. The distinguishing feature of this formalization is that it remains close to the textbook proofs that are based on proving the correctness

Abstract. This work presents a general methodology for verification of the completeness of firstorder unification algorithms à la Robinson developed in the higher-order proof assistant PVS. The methodology is based on a previously developed formalization of the theorem of existence of most general

The Duration Calculus (DC) is an interval temporal logic for reasoning about real-time systems. This paper describes a tool for constructing DC specifications and checking DC proofs. The proof assistant is implemented by encoding the semantics of DC within the higherorder logic of a general

Abstract. Our general goal is to provide better automation in interactive proof assistants such as Coq. We present an interpreter of proof traces in first-order multi-sorted logic with equality. Thanks to the reflection ability of Coq, this interpreter is both implemented and formally proved sound

The Duration Calculus (DC) is an interval temporal logic for reasoning about real-time systems. This paper describes a tool for constructing DC specifications and checking DC proofs. The proof assistant is implemented by encoding the semantics of DC within the higherorder logic of a general

In this article, we adopt a very pragmatic and modest approach to the challenge of improving proof automation in Coq: we simply accept the above two

-modal sequent inference system, which uses unification (or constraint-satisfaction) to resolve the values of variables, in the style of [Voronkov, 1996]. From one point of view, this report can be regarded as the multimodal generalization of the results presented for linear logic and first-order modal logic