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

was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory

In this paper, we describe an approach to theorem proving in Computational Tree Logic (CTL) which utilises classical first-order resolution techniques. Since there already exist a lot of well-developed first-order logic theorem provers, reusing those techniques provides great benefit for solving

uncertainty renders classical first-order logic inadequate for many important classes of problems. General-purpose languages are beginning to emerge for which the fundamental logical basis is probability. Increasingly expressive probabilistic languages demand a theoretical foundation that fully integrates

First-order Automated Theorem Proving (ATP) is one of the oldest and most developed areas of automated reasoning. Today, the most widely used first-order provers are fully automatic and process first-order logic with equality. Many state-of-the-art ATP systems consist of a clausifier, translating a

Writing (meta-)programs that manipulate other (object-) programs poses significant technical problems when the objectlanguage itself has a notion of binders and variable occurrences. Higher-order abstract syntax is a representation of object programs that has recently been the focus of several

is filtered through a buffer or a queue, possibly with feedback. In a series of theorems, we give necessary and sufficient conditions for each of these notions in the form of simple first-order or second-order axioms. We illustrate the formalism by applying it to asynchronous CCS and the core join calculus.

frames and we offer a general completeness result in terms of them which circumvents some well-known prob-lems of propositional and first order neighborhood semantics (mainly the fact that many classical modal logics are incomplete with respect to an unmodified version of neighbor-hood frames). We argue

implementation of hyper-linking which addresses many of the inefficiencies of round-by-round hyper-linking encountered when adding special methods in support of equality. Smallest instance first hyper-linking is based on the formalization of generating smallest clauses first, a heuristic widely used in other

There have been many proposals for first-order belief networks (i.e., where we quantify over individuals) but these typically only let us reason about the individuals that we know about. There are many instances where we have to quantify over all of the individuals in a population. When we do