Search results for "Logic in computer science"
showing 9 items of 129 documents
Détection des fonctions de rang linéaires à terme
2013
Program termination is a hot research topic in program analysis. The last a few years have witnessed the development of termination analyzers for programming languages such as C and Java with remarkable precision and performance. These systems are largely based on techniques and tools coming from the field of constraint programming. In this paper, we first recall an algorithm based on Farkas' Lemma for discovering linear ranking functions proving termination of a certain class of loops. Then we propose an extension of this method for showing the existence of eventual linear ranking functions, i.e., linear functions that become ranking functions after a finite unrolling of the loop. We show …
De l'usage des logiques modales pour la gestion de l'incertitude des données : application en archéologie
2015
Archaeological information systems offer methods and tools for representing collected data and performing analyses with which taking into account imperfect data is often hard to please. Our contribution describes the use of several modal logics to model and verify the effects of the consideration of uncertain data, but also to check the quality of a corpus in an in-terdisciplinary collaborative environment. The modelling and the reasoning based on uncertain data, which are studied in this article, are integrated open and extensible platform allowing to manage archaeological data. From the computing point of view, the reasoner used, based on the first order logic, provides the archaeologists…
Full CNF Encoding: The Counting Constraints Case
2004
Many problems are naturally expressed using CNF clauses and boolean cardinality constraints. It is generally believed that solving such problems through pure CNF encoding is inefficient, so many authors has proposed specialized algorithms : the pseudo-boolean solvers. In this paper we show that an appropriate pure CNF encoding can be competitive with these specialized methods. In conjunction with our encoding, we propose a slight modification of the DLL procedure that allows any DLL-based SAT solver to solve boolean cardinality optimization problems. We show experimentally that our encoding allows zchaff to be competitive with pseudo-boolean solvers on some decision and optimization problem…
The Syllogistic with Unity
2011
We extend the language of the classical syllogisms with the sentence-forms “At most 1 p is a q” and “More than 1 p is a q”. We show that the resulting logic does not admit a finite set of syllogism-like rules whose associated derivation relation is sound and complete, even when reductio ad absurdum is allowed.
Simafield : Un logiciel de modélisation spatiale de scènes agronomiques
2013
Environmental measures lead farmers to use more and more decision support tools to reduce their chemical inputs without losing yield. Imaging system based on crop/weed discrimination algorithms have been developed to detect weeds in field and allow a site specific spraying. These algorithms needs to be thoroughly evaluated before considering a public release and current evaluation are based on real images and are very tedious. SimAField is a software that aims at modeling agronomic fields with crop and weeds and simulate the picture taking process to replace ground truth and allow an automated evaluation of crop/weed discrimination algorithms.
Very narrow quantum OBDDs and width hierarchies for classical OBDDs
2014
In the paper we investigate a model for computing of Boolean functions - Ordered Binary Decision Diagrams (OBDDs), which is a restricted version of Branching Programs. We present several results on the comparative complexity for several variants of OBDD models. - We present some results on the comparative complexity of classical and quantum OBDDs. We consider a partial function depending on a parameter k such that for any k > 0 this function is computed by an exact quantum OBDD of width 2, but any classical OBDD (deterministic or stable bounded-error probabilistic) needs width 2 k+1. - We consider quantum and classical nondeterminism. We show that quantum nondeterminism can be more efficien…
Modal Consequence Relations Extending S4.3: An Application of Projective Unification
2016
We characterize all finitary consequence relations over $\mathbf{S4.3}$ , both syntactically, by exhibiting so-called (admissible) passive rules that extend the given logic, and semantically, by providing suitable strongly adequate classes of algebras. This is achieved by applying an earlier result stating that a modal logic $L$ extending $\mathbf{S4}$ has projective unification if and only if $L$ contains $\mathbf{S4.3}$ . In particular, we show that these consequence relations enjoy the strong finite model property, and are finitely based. In this way, we extend the known results by Bull and Fine, from logics, to consequence relations. We also show that the lattice of consequence relation…
Introduction to Mathematical Logic, Edition 2021
2021
Textbook for students in mathematical logic. First order languages. Axioms of constructive and classical logic. Proving formulas in propositional and predicate logic. Glivenko's theorem and constructive embedding. Axiom independence. Interpretations, models and completeness theorems. Normal forms. Tableaux and resolution methods. Herbrand's theorem. Sections 1, 2, 3 represent an extended translation of the corresponding chapters of the book: V. Detlovs, Elements of Mathematical Logic, Riga, University of Latvia, 1964, 252 pp. (in Latvian).
A Completeness Proof for a Regular Predicate Logic with Undefined Truth Value
2023
We provide a sound and complete proof system for an extension of Kleene's ternary logic to predicates. The concept of theory is extended with, for each function symbol, a formula that specifies when the function is defined. The notion of "is defined" is extended to terms and formulas via a straightforward recursive algorithm. The "is defined" formulas are constructed so that they themselves are always defined. The completeness proof relies on the Henkin construction. For each formula, precisely one of the formula, its negation, and the negation of its "is defined" formula is true on the constructed model. Many other ternary logics in the literature can be reduced to ours. Partial functions …