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.

scholarly journals Towards closed world reasoning in dynamic open worlds

2010 ◽  
Vol 10 (4-6) ◽  
pp. 547-563 ◽  
Author(s):  
MARTIN SLOTA ◽  
JOÃO LEITE
Keyword(s):  
Semantic Web ◽  
State Of The Art ◽  
Knowledge Bases ◽  
Order Logic ◽  
First Order Logic ◽  
Static Case ◽  
First Order ◽  
Closed World ◽  
Hybrid Knowledge ◽  
First Time

AbstractThe need for integration of ontologies with nonmonotonic rules has been gaining importance in a number of areas, such as the Semantic Web. A number of researchers addressed this problem by proposing a unified semantics forhybrid knowledge basescomposed of both an ontology (expressed in a fragment of first-order logic) and nonmonotonic rules. These semantics have matured over the years, but only provide solutions for the static case when knowledge does not need to evolve.In this paper we take a first step towards addressing the dynamics of hybrid knowledge bases. We focus on knowledge updates and, considering the state of the art of belief update, ontology update and rule update, we show that current solutions are only partial and difficult to combine. Then we extend the existing work on ABox updates with rules, provide a semantics for such evolving hybrid knowledge bases and study its basic properties.To the best of our knowledge, this is the first time that an update operator is proposed for hybrid knowledge bases.

Principles and practice in verifying rule-based systems

1992 ◽  
Vol 7 (2) ◽  
pp. 115-141 ◽  
Author(s):  
Alun D. Preece ◽  
Rajjan Shinghal ◽  
Aïda Batarekh
Keyword(s):  
Expert System ◽  
Knowledge Base ◽  
State Of The Art ◽  
Knowledge Bases ◽  
Order Logic ◽  
First Order Logic ◽  
Rule Based ◽  
First Order ◽  
Rule Bases ◽  
System Knowledge

AbstractThis paper surveys the verification of expert system knowledge bases by detecting anomalies. Such anomalies are highly indicative of errors in the knowledge base. The paper is in two parts. The first part describes four types of anomaly: redundancy, ambivalence, circularity, and deficiency. We consider rule bases which are based on first-order logic, and explain the anomalies in terms of the syntax and semantics of logic. The second part presents a review of five programs which have been built to detect various subsets of the anomalies. The four anomalies provide a framework for comparing the capabilities of the five tools, and we highlight the strengths and weaknesses of each approach. This paper therefore provides not only a set of underlying principles for performing knowledge base verification through anomaly detection, but also a survey of the state-of-the-art in building practical tools for carrying out such verification. The reader of this paper is expected to be familiar with first-order logic.

AUTOMATED TERMINATION IN MODEL-CHECKING MODULO THEORIES

2013 ◽  
Vol 24 (02) ◽  
pp. 211-232 ◽  
Author(s):  
ALESSANDRO CARIONI ◽  
SILVIO GHILARDI ◽  
SILVIO RANISE
Keyword(s):  
Model Checking ◽  
Sufficient Conditions ◽  
Order Logic ◽  
Satisfiability Modulo Theories ◽  
First Order Logic ◽  
Reachability Problem ◽  
First Order ◽  
Recent Advances ◽  
Infinite State Systems ◽  
Infinite State

We identify sufficient conditions to automatically establish the termination of a backward reachability procedure for infinite state systems by using well-quasi-orderings. Besides showing that backward reachability succeeds on many instances of problems covered by general termination results, we argue that it could predict termination also on interesting instances of the reachability problem that are outside the scope of applicability of such general results. We work in the declarative framework of Model Checking Modulo Theories that permits us to exploit recent advances in Satisfiability Modulo Theories solving and model-theoretic notions of first-order logic.

scholarly journals COMPLETENESS AND CATEGORICITY (IN POWER): FORMALIZATION WITHOUT FOUNDATIONALISM

2014 ◽  
Vol 20 (1) ◽  
pp. 39-79 ◽  
Author(s):  
JOHN T. BALDWIN
Keyword(s):  
Formal Methods ◽  
Model Theory ◽  
Second Order ◽  
Order Logic ◽  
First Order Logic ◽  
Specific Content ◽  
First Order ◽  
Complete Theories ◽  
The Stability ◽  
Second Order Logic

AbstractWe propose a criterion to regard a property of a theory (in first or second order logic) as virtuous: the property must have significant mathematical consequences for the theory (or its models). We then rehearse results of Ajtai, Marek, Magidor, H. Friedman and Solovay to argue that for second order logic, ‘categoricity’ has little virtue. For first order logic, categoricity is trivial; but ‘categoricity in power’ has enormous structural consequences for any of the theories satisfying it. The stability hierarchy extends this virtue to other complete theories. The interaction of model theory and traditional mathematics is examined by considering the views of such as Bourbaki, Hrushovski, Kazhdan, and Shelah to flesh out the argument that the main impact of formal methods on mathematics is using formal definability to obtain results in ‘mainstream’ mathematics. Moreover, these methods (e.g., the stability hierarchy) provide an organization for much mathematics which gives specific content to dreams of Bourbaki about the architecture of mathematics.

scholarly journals Satisfiability Checking and Query Answering for Large Ontologies

10.29007/n1sv ◽  
2018 ◽  
Author(s):  
Christoph Weidenbach ◽  
Patrick Wischnewski
Keyword(s):  
State Of The Art ◽  
The State ◽  
Order Logic ◽  
Query Answering ◽  
First Order Logic ◽  
First Order ◽  
Satisfiability Checking ◽  
Superposition Calculus

In this paper we develop a sound, complete and terminating superposition calculusplus a query answering calculus for the BSH-Y2 fragment of theBernays-Schoenfinkel Horn class of first-order logic.BSH-Y2 can be used to represent expressive ontologies.In addition to checking consistency, our calculus supports query answeringfor queries with arbitrary quantifier alternations.Experiments on BSH-Y2 (fragments) of several large ontologies show that ourapproach advances the state of the art.

scholarly journals Model-Finding for Externally Verifying FOL Ontologies: A Study of Spatial Ontologies

2020 ◽  
Author(s):  
Shirly Stephen ◽  
Torsten Hahmann
Keyword(s):  
Systematic Study ◽  
State Of The Art ◽  
Order Logic ◽  
First Order Logic ◽  
Problem Size ◽  
Effective Measure ◽  
First Order ◽  
Highly Effective ◽  
Model Finding ◽  
Synthetic Datasets

Use and reuse of an ontology requires prior ontology verification which encompasses, at least, proving that the ontology is internally consistent and consistent with representative datasets. First-order logic (FOL) model finders are among the only available tools to aid us in this undertaking, but proving consistency of FOL ontologies is theoretically intractable while also rarely succeeding in practice, with FOL model finders scaling even worse than FOL theorem provers. This issue is further exacerbated when verifying FOL ontologies against datasets, which requires constructing models with larger domain sizes. This paper presents a first systematic study of the general feasibility of SAT-based model finding with FOL ontologies. We use select spatial ontologies and carefully controlled synthetic datasets to identify key measures that determine the size and difficulty of the resulting SAT problems. We experimentally show that these measures are closely correlated with the runtimes of Vampire and Paradox, two state-of-the-art model finders. We propose a definition elimination technique and demonstrate that it can be a highly effective measure for reducing the problem size and improving the runtime and scalability of model finding.

scholarly journals Checking Foundational Proof Certificates for First-Order Logic (Extended Abstract)

10.29007/7gnr ◽  
2018 ◽  
Author(s):  
Zakaria Chihani ◽  
Dale Miller ◽  
Fabien Renaud
Keyword(s):  
Programming Language ◽  
Logic Program ◽  
Formal Proof ◽  
Higher Order ◽  
Order Logic ◽  
Higher Order Logic ◽  
Backtracking Search ◽  
First Order ◽  
Proof Checker ◽  
Prolog Programming

We present the design philosophy of a proof checker based on a notion of foundational proof certificates. At the heart of this design is a semantics of proof evidence that arises from recent advances in the theory of proofs for classical and intuitionistic logic. That semantics is then performed by a (higher-order) logic program: successful performance means that a formal proof of a theorem has been found. We describe how the lambda Prolog programming language provides several features that help guarantee such a soundness claim. Some of these features (such as strong typing, abstract datatypes, and higher-order programming) were features of the ML programming language when it was first proposed as a proof checker for LCF. Other features of lambda Prolog (such as support for bindings, substitution, and backtracking search) turn out to be equally important for describing and checking the proof evidence encoded in proof certificates. Since trusting our proof checker requires trusting a programming language implementation, we discuss various avenues for enhancing one's trust of such a checker.

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