相关论文: Redundancy in Logic I: CNF Propositional Formulae

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…

Advancements in computer science and AI lead to the development of larger, more complex knowledge bases. These are susceptible to contradictions, particularly when multiple experts are involved. To ensure integrity during changes,…

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…

Code-trained language models have proven to be highly effective for various code intelligence tasks. However, they can be challenging to train and deploy for many software engineering applications due to computational bottlenecks and memory…

Forgetting a belief acquisition episode may not cause information loss because of the others. Checking whether it does is not obvious, as the contribution of each belief revision is not isolated from the others, and the same information may…

Log-linear models are typically fitted to contingency table data to describe and identify the relationship between different categorical variables. However, the data may include observed zero cell entries. The presence of zero cell entries…

Model-checking resource logics with production and consumption of resources is a computationally hard and often undecidable problem. We introduce a simple and realistic assumption that there is at least one diminishing resource, that is, a…

Properties expressed as the provability of a first-order sentence can be disproved by just finding a model of the negation of the sentence. This fact, however, is meaningful in restricted cases only, depending on the shape of the sentence…

Blocked clauses provide the basis for powerful reasoning techniques used in SAT, QBF, and DQBF solving. Their definition, which relies on a simple syntactic criterion, guarantees that they are both redundant and easy to find. In this paper,…

Consistent answers to a query from a possibly inconsistent database are answers that are simultaneously retrieved from every possible repair of the database. Repairs are consistent instances that minimally differ from the original…

Redundancy elimination is one of the crucial ingredients of efficient saturation-based proof search. We improve redundancy elimination by introducing a new notion of redundancy, based on partial clauses and redundancy formulas, which is…

We show that SCL(FOL) can simulate the derivation of non-redundant clauses by superposition for first-order logic without equality. Superposition-based reasoning is performed with respect to a fixed reduction ordering. The completeness…

We survey the different properties of an intuitive notion of redundancy, as a function of the precise semantics given to the notion of partial implication. The final version of this survey will appear in the Proceedings of the Int. Conf.…

We propose a norm of consistency for a mixed set of defeasible and strict sentences, based on a probabilistic semantics. This norm establishes a clear distinction between knowledge bases depicting exceptions and those containing outright…

Conditional-independence-based discovery uses statistical tests to identify a graphical model that represents the independence structure of variables in a dataset. These tests, however, can be unreliable, and algorithms are sensitive to…

A relational database is inconsistent if it does not satisfy a given set of integrity constraints. Nevertheless, it is likely that most of the data in it is consistent with the constraints. In this paper we apply logic programming based on…

We initiate an investigation how the fundamental concept of independence can be represented effectively in the presence of incomplete information in relational databases. The concepts of possible and certain independence are proposed, and…

Earlier, we introduced Partial Quantifier Elimination (PQE). It is a $\mathit{generalization}$ of regular quantifier elimination where one can take a $\mathit{part}$ of the formula out of the scope of quantifiers. We apply PQE to CNF…

In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The…

The question whether an ontology can safely be replaced by another, possibly simpler, one is fundamental for many ontology engineering and maintenance tasks. It underpins, for example, ontology versioning, ontology modularization,…