Related papers: The Complexity of Propositional Implication
We study the isomorphic implication problem for Boolean constraints. We show that this is a natural analog of the subgraph isomorphism problem. We prove that, depending on the set of constraints, this problem is in P, NP-complete, or…
We examine the complexity of inference in Bayesian networks specified by logical languages. We consider representations that range from fragments of propositional logic to function-free first-order logic with equality; in doing so we cover…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
This paper is devoted to the investigation of term-definable connexive implications in substructural logics with exchange and, on the semantical perspective, in sub-varieties of commutative residuated lattices (FLe-algebras). In particular,…
Both propositional dependence logic and inquisitive logic are expressively complete. As a consequence, every formula with intuitionistic disjunction or intuitionistic implication can be translated equivalently into a formula in the language…
In 1978, Schaefer proved his famous dichotomy theorem for generalized satisfiability problems. He defined an infinite number of propositional satisfiability problems (nowadays usually called Boolean constraint satisfaction problems) and…
In order to prove that the P of problems is different to the NP class, we consider the satisfability problem of propositional calculus formulae, which is an NP-complete problem. It is shown that, for every search algorithm A, there is a set…
Linear representations for a subclass of boolean symmetric functions selected by a parity condition are shown to constitute a generalization of the linear constraints on probabilities introduced by Boole. These linear constraints are…
We give a complexity dichotomy for the problem of computing the partition function of a weighted Boolean constraint satisfaction problem. Such a problem is parameterized by a set of rational-valued functions, which generalize constraints.…
In this article we treat a notion of continuity for a multi-valued function F and we compute the descriptive set-theoretic complexity of the set of all x for which F is continuous at x. We give conditions under which the latter set is…
We determine all composition-closed equational classes of Boolean functions. These classes provide a natural generalization of clones and iterative algebras: they are closed under composition, permutation and identification…
In our setting enumeration amounts to generate all solutions of a problem instance without duplicates. We address the problem of enumerating the models of B-formulae. A B-formula is a propositional formula whose connectives are taken from a…
In this paper, we investigate the extent to which knowledge compilation can be used to improve inference from propositional weighted bases. We present a general notion of compilation of a weighted base that is parametrized by any…
The subsumption problem with respect to terminologies in the description logic ALC is EXPTIME-complete. We investigate the computational complexity of fragments of this problem by means of allowed Boolean operators. Hereto we make use of…
We give a comprehensive account on the parameterized complexity of model checking and satisfiability of propositional inclusion and independence logic. We discover that for most parameterizations the problems are either in FPT or…
It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…
We study implicational formulas in the context of proof complexity of intuitionistic propositional logic (IPC). On the one hand, we give an efficient transformation of tautologies to implicational tautologies that preserves the lengths of…
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
Here, in a series of articles, we show methods for calculating propositional statements using algebraic polynomials as symbols for the connectives, which are named operators. These polynomials originate from the transformation between the…