Related papers: Stellar Resolution: Multiplicatives
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
Many applications of denotational semantics, such as higher-order model checking or the complexity of normalization, rely on finite semantics for monomorphic type systems. We exhibit such a finite semantics for a polymorphic purely linear…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
Mixed integer linear programming (MILP) is a powerful representation often used to formulate decision-making problems under uncertainty. However, it lacks a natural mechanism to reason about objects, classes of objects, and relations.…
We study the expressivity and computational aspects of first-order logic and its extensions in the semiring semantics developed by Gr\"adel and Tannen. We characterize the complexity of model checking and data complexity of first-order…
This paper focuses on resolution in linguistic first order logic with truth value taken from linear symmetrical hedge algebra. We build the basic components of linguistic first order logic, including syntax and semantics. We present a…
This paper deals with a problem from discrete-time robust control which requires the solution of constraints over the reals that contain both universal and existential quantifiers. For solving this problem we formulate it as a program in a…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…
A multi-domain spectral method for computing very high precision 3-D stellar models is presented. The boundary of each domain is chosen in order to coincide with a physical discontinuity (e.g. the star's surface). In addition, a…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
By means of the generating function method, a linear recurrence relation is explicitly resolved. The solution is expressed in terms of the Stirling numbers of both the first and the second kind. Two remarkable pairs of combinatorial…
An algorithm for computing the stable model semantics of logic programs is developed. It is shown that one can extend the semantics and the algorithm to handle new and more expressive types of rules. Emphasis is placed on the use of…
Resolution modulo is a first-order theorem proving method that can be applied both to first-order presentations of simple type theory (also called higher-order logic) and to set theory. When it is applied to some first-order presentations…
Full first order linear logic can be presented as an abstract logic programming language in Miller's system Forum, which yields a sensible operational interpretation in the 'proof search as computation' paradigm. However, Forum still has to…
We introduce a proper display calculus for first-order logic, of which we prove soundness, completeness, conservativity, subformula property and cut elimination via a Belnap-style metatheorem. All inference rules are closed under uniform…
Modular logic programs provide a way of viewing logic programs as consisting of many independent, meaningful modules. This paper introduces first-order modular logic programs, which can capture the meaning of many answer set programs. We…
We consider a first-order logic for the integers with addition. This logic extends classical first-order logic by modulo-counting, threshold-counting and exact-counting quantifiers, all applied to tuples of variables (here, residues are…
It is well known that for a first order system of linear difference equations with rational function coefficients, a solution that is holomorphic in some left half plane can be analytically continued to a meromorphic solution in the whole…
The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…
We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which…