Automated Reasoning Support for First-Order Ontologies

2006 ◽  
pp. 18-32 ◽  
Author(s):  
Peter Baumgartner ◽  
Fabian M. Suchanek
Keyword(s):  
Automated Reasoning ◽  
First Order

scholarly journals Model Completeness, Uniform Interpolants and Superposition Calculus

2021 ◽  
Author(s):  
Diego Calvanese ◽  
Silvio Ghilardi ◽  
Alessandro Gianola ◽  
Marco Montali ◽  
Andrey Rivkin
Keyword(s):  
Automated Reasoning ◽  
Quantifier Elimination ◽  
Effective Solution ◽  
Model Completeness ◽  
Present Contribution ◽  
First Order ◽  
Reduction Strategies ◽  
Infinite State Systems ◽  
Infinite State ◽  
Superposition Calculus

AbstractUniform interpolants have been largely studied in non-classical propositional logics since the nineties; a successive research line within the automated reasoning community investigated uniform quantifier-free interpolants (sometimes referred to as “covers”) in first-order theories. This further research line is motivated by the fact that uniform interpolants offer an effective solution to tackle quantifier elimination and symbol elimination problems, which are central in model checking infinite state systems. This was first pointed out in ESOP 2008 by Gulwani and Musuvathi, and then by the authors of the present contribution in the context of recent applications to the verification of data-aware processes. In this paper, we show how covers are strictly related to model completions, a well-known topic in model theory. We also investigate the computation of covers within the Superposition Calculus, by adopting a constrained version of the calculus and by defining appropriate settings and reduction strategies. In addition, we show that computing covers is computationally tractable for the fragment of the language used when tackling the verification of data-aware processes. This observation is confirmed by analyzing the preliminary results obtained using the mcmt tool to verify relevant examples of data-aware processes. These examples can be found in the last version of the tool distribution.

scholarly journals Exploring Steinitz-Rademacher Polyhedra: a Challenge for Automated Reasoning Tools

10.29007/d3ls ◽  
2018 ◽  
Author(s):  
Jesse Alama
Keyword(s):  
Automated Reasoning ◽  
Order Theory ◽  
Incidence Structures ◽  
First Order ◽  
First Order Theory

This note reports on some experiments, using a handful of standard automated reasoning tools, for exploring Steinitz-Rademacher polyhedra, which are models of a certain first-order theory of incidence structures. This theory and its models, even simple ones, presents significant, geometrically fascinating challenges for automated reasoning tools are.

scholarly journals Reasoning Inside The Box: Deduction in Herbrand Logics

10.29007/kx2m ◽  
2018 ◽  
Author(s):  
Liron Cohen ◽  
Yoni Zohar
Keyword(s):  
Automated Reasoning ◽  
Proof System ◽  
First Order ◽  
Proof Systems ◽  
The Rich ◽  
Order Structures ◽  
Effective Proof

Herbrand structures are a subclass of standard first-order structures commonly used in logic and automated reasoning due to their strong definitional character. This paper is devoted to the logics induced by them: Herbrand and semi-Herbrand logics, with and without equality. The rich expressiveness of these logics entails that there is no adequate effective proof system for them. We therefore introduce infinitary proof systems for Herbrand logics, and prove their completeness. Natural and sound finitary approximations of the infinitary systems are also presented.

scholarly journals Generalized Completeness for SOS Resolution and its Application to a New Notion of Relevance

2021 ◽  
pp. 327-343
Author(s):  
Fajar Haifani ◽  
Sophie Tourret ◽  
Christoph Weidenbach
Keyword(s):  
Automated Reasoning ◽  
First Order ◽  
Completeness Result ◽  
Resolution Refutation ◽  
Unsatisfiable Core

AbstractWe prove the SOS strategy for first-order resolution to be refutationally complete on a clause set N and set-of-support S if and only if there exists a clause in S that occurs in a resolution refutation from $$N\cup S$$ N ∪ S . This strictly generalizes and sharpens the original completeness result requiring N to be satisfiable. The generalized SOS completeness result supports automated reasoning on a new notion of relevance aiming at capturing the support of a clause in the refutation of a clause set. A clause C is relevant for refuting a clause set N if C occurs in every refutation of N. The clause C is semi-relevant, if it occurs in some refutation, i.e., if there exists an SOS refutation with set-of-support $$S = \{C\}$$ S = { C } from $$N\setminus \{C\}$$ N \ { C } . A clause that does not occur in any refutation from N is irrelevant, i.e., it is not semi-relevant. Our new notion of relevance separates clauses in a proof that are ultimately needed from clauses that may be replaced by different clauses. In this way it provides insights towards proof explanation in refutations beyond existing notions such as that of an unsatisfiable core.

scholarly journals Automated reasoning-alternative methods

2004 ◽  
Vol 1 (3) ◽  
pp. 15-20
Author(s):  
Aleksandar Perovic ◽  
Nedeljko Stefanovic ◽  
Milos Milosevic ◽  
Dejan Ilic
Keyword(s):  
Automated Reasoning ◽  
Quantifier Elimination ◽  
Order Theory ◽  
Alternative Methods ◽  
Formal Representation ◽  
First Order ◽  
First Order Theory ◽  
Interpretation Method

Our main goal is to describe a potential usage of the interpretation method (i.e. formal representation of one first order theory into another) together with quantifier elimination procedures developed in the GIS.

scholarly journals Handling Transitive Relations in First-Order Automated Reasoning

2021 ◽  
Author(s):  
Koen Claessen ◽  
Ann Lillieström
Keyword(s):  
Automated Reasoning ◽  
Equivalence Relations ◽  
Binary Relations ◽  
First Order ◽  
Total Orders

AbstractWe present a number of alternative ways of handling transitive binary relations that commonly occur in first-order problems, in particular equivalence relations, total orders, and transitive relations in general. We show how such relations can be discovered syntactically in an input theory, and how they can be expressed in alternative ways. We experimentally evaluate different such ways on problems from the TPTP, using resolution-based reasoning tools as well as instance-based tools. Our conclusions are that (1) it is beneficial to consider different treatments of binary relations as a user, and that (2) reasoning tools could benefit from using a preprocessor or even built-in support for certain types of binary relations.

scholarly journals On Conflict-Driven Reasoning

10.29007/spwm ◽  
2018 ◽  
Author(s):  
Maria Paola Bonacina
Keyword(s):  
Formal Methods ◽  
Automated Reasoning ◽  
State Of The Art ◽  
Research Direction ◽  
Order Logic ◽  
Satisfiability Modulo Theories ◽  
Backtracking Search ◽  
First Order ◽  
Clause Learning ◽  
A Current

Automated formal methods and automated reasoning are interconnected, as formal methods generate reasoning problems and incorporate reasoning techniques. For example, formal methods tools employ reasoning engines to find solutions of sets of constraints, or proofs of conjectures. From a reasoning perspective, the expressivity of the logical lan- guage is often directly proportional to the difficulty of the problem. In propositional logic, Conflict-Driven Clause Learning (CDCL) is one of the key features of state-of-the-art sat- isfiability solvers. The idea is to restrict inferences to those needed to explain conflicts, and use conflicts to prune a backtracking search. A current research direction in auto- mated reasoning is to generalize this notion of conflict-driven satisfiability to a paradigm of conflict-driven reasoning in first-order theories for satisfiability modulo theories and as- signments, and even in full first-order logic for generic automated theorem proving. While this is a promising and exciting lead, it also poses formidable challenges.

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