Towards an automated deduction system for first-order possibilistic logic programming with fuzzy constants

2002 ◽  
Vol 17 (9) ◽  
pp. 887-924 ◽  
Author(s):  
Teresa Alsinet ◽  
Llu�s Godo
Keyword(s):  
Logic Programming ◽  
Automated Deduction ◽  
Deduction System ◽  
First Order ◽  
Possibilistic Logic

Logics for the Semantic Web

2011 ◽  
pp. 24-43
Author(s):  
J. Bruijn
Keyword(s):  
Semantic Web ◽  
Logic Programming ◽  
Description Logic ◽  
Description Logics ◽  
Order Logic ◽  
First Order Logic ◽  
Horn Logic ◽  
First Order ◽  
Logical Language ◽  
Rule Languages

This chapter introduces a number of formal logical languages which form the backbone of the Semantic Web. They are used for the representation of both ontologies and rules. The basis for all languages presented in this chapter is the classical first-order logic. Description logics is a family of languages which represent subsets of first-order logic. Expressive description logic languages form the basis for popular ontology languages on the Semantic Web. Logic programming is based on a subset of first-order logic, namely Horn logic, but uses a slightly different semantics and can be extended with non-monotonic negation. Many Semantic Web reasoners are based on logic programming principles and rule languages for the Semantic Web based on logic programming are an ongoing discussion. Frame Logic allows object-oriented style (frame-based) modeling in a logical language. RuleML is an XML-based syntax consisting of different sublanguages for the exchange of specifications in different logical languages over the Web.

Lifting propositional proof compression algorithms to first-order logic

2020 ◽  
Author(s):  
Jan Gorzny ◽  
Ezequiel Postan ◽  
Bruno Woltzenlogel Paleo
Keyword(s):  
Propositional Logic ◽  
Empirical Evaluation ◽  
Order Logic ◽  
Automated Deduction ◽  
First Order Logic ◽  
Compression Algorithms ◽  
International Conference ◽  
First Order ◽  
Theorem Provers ◽  
Resolution Proofs

Abstract Proofs are a key feature of modern propositional and first-order theorem provers. Proofs generated by such tools serve as explanations for unsatisfiability of statements. However, these explanations are complicated by proofs which are not necessarily as concise as possible. There are a wide variety of compression techniques for propositional resolution proofs but fewer compression techniques for first-order resolution proofs generated by automated theorem provers. This paper describes an approach to compressing first-order logic proofs based on lifting proof compression ideas used in propositional logic to first-order logic. The first approach lifted from propositional logic delays resolution with unit clauses, which are clauses that have a single literal. The second approach is partial regularization, which removes an inference $\eta $ when it is redundant in the sense that its pivot literal already occurs as the pivot of another inference in every path from $\eta $ to the root of the proof. This paper describes the generalization of the algorithms LowerUnits and RecyclePivotsWithIntersection (Fontaine et al.. Compression of propositional resolution proofs via partial regularization. In Automated Deduction—CADE-23—23rd International Conference on Automated Deduction, Wroclaw, Poland, July 31–August 5, 2011, p. 237--251. Springer, 2011) from propositional logic to first-order logic. The generalized algorithms compresses resolution proofs containing resolution and factoring inferences with unification. An empirical evaluation of these approaches is included.

A proof-theoretic treatment of λ-reduction with cut-elimination: λ-calculus as a logic programming language

2011 ◽  
Vol 76 (2) ◽  
pp. 673-699 ◽  
Author(s):  
Michael Gabbay
Keyword(s):  
Logic Programming ◽  
Programming Language ◽  
Functional Programming ◽  
Order Logic ◽  
First Order Logic ◽  
Cut Elimination ◽  
Logic Programming Language ◽  
First Order ◽  
Functional Programming Language ◽  
Sequent System

AbstractWe build on an existing a term-sequent logic for the λ-calculus. We formulate a general sequent system that fully integrates αβη-reductions between untyped λ-terms into first order logic.We prove a cut-elimination result and then offer an application of cut-elimination by giving a notion of uniform proof for λ-terms. We suggest how this allows us to view the calculus of untyped αβ-reductions as a logic programming language (as well as a functional programming language, as it is traditionally seen).

scholarly journals XPath-logic and XPathLog: A logic-programming style XML data manipulation language

2004 ◽  
Vol 4 (3) ◽  
pp. 239-287 ◽  
Author(s):  
WOLFGANG MAY
Keyword(s):  
Logic Programming ◽  
Data Model ◽  
Formal Semantics ◽  
Xml Data ◽  
First Order ◽  
Answer Set Semantics ◽  
Manipulation Language ◽  
Horn Fragment ◽  
Main Language

We define XPathLog as a Datalog-style extension of XPath. XPathLog provides a clear, declarative language for querying and manipulating XML whose perspectives are especially in XML data integration. In our characterization, the formal semantics is defined wrt. an edge-labeled graph-based model, which covers the XML data model. We give a complete, logic-based characterization of XML data and the main language concept for XML, XPath. XPath-Logic extends the XPath language with variable bindings and embeds it into first-order logic. XPathLog is then the Horn fragment of XPath-Logic, providing a Datalog-style, rule-based language for querying and manipulating XML data. The model-theoretic semantics of XPath-Logic serves as the base of XPathLog as a logic-programming language, whereas also an equivalent answer-set semantics for evaluating XPathLog queries is given. In contrast to other approaches, the XPath syntax and semantics is also used for a declarative specification how the database should be updated: when used in rule heads, XPath filters are interpreted as specifications of elements and properties which should be added to the database.

scholarly journals The PITA system: Tabling and answer subsumption for reasoning under uncertainty

2011 ◽  
Vol 11 (4-5) ◽  
pp. 433-449 ◽  
Author(s):  
FABRIZIO RIGUZZI ◽  
TERRANCE SWIFT
Keyword(s):  
Logic Programming ◽  
Probabilistic Logic ◽  
Similar Distribution ◽  
Logic Programs ◽  
Reasoning Under Uncertainty ◽  
Complex Queries ◽  
Possibilistic Logic ◽  
Distribution Semantics ◽  
Measure Of Uncertainty ◽  
Very High

AbstractMany real world domains require the representation of a measure of uncertainty. The most common such representation is probability, and the combination of probability with logic programs has given rise to the field of Probabilistic Logic Programming (PLP), leading to languages such as the Independent Choice Logic, Logic Programs with Annotated Disjunctions (LPADs), Problog, PRISM, and others. These languages share a similar distribution semantics, and methods have been devised to translate programs between these languages. The complexity of computing the probability of queries to these general PLP programs is very high due to the need to combine the probabilities of explanations that may not be exclusive. As one alternative, the PRISM system reduces the complexity of query answering by restricting the form of programs it can evaluate. As an entirely different alternative, Possibilistic Logic Programs adopt a simpler metric of uncertainty than probability.Each of these approaches—general PLP, restricted PLP, and Possibilistic Logic Programming—can be useful in different domains depending on the form of uncertainty to be represented, on the form of programs needed to model problems, and on the scale of the problems to be solved. In this paper, we show how the PITA system, which originally supported the general PLP language of LPADs, can also efficiently support restricted PLP and Possibilistic Logic Programs. PITA relies on tabling with answer subsumption and consists of a transformation along with an API for library functions that interface with answer subsumption. We show that, by adapting its transformation and library functions, PITA can be parameterized to PITA(IND, EXC) which supports the restricted PLP of PRISM, including optimizations that reduce non-discriminating arguments and the computation of Viterbi paths. Furthermore, we show PITA to be competitive with PRISM for complex queries to Hidden Markov Model examples, and sometimes much faster. We further show how PITA can be parameterized to PITA(COUNT) which computes the number of different explanations for a subgoal, and to PITA(POSS) which scalably implements Possibilistic Logic Programming. PITA is a supported package in version 3.3 of XSB.

scholarly journals Proof systems for Geometric theories (PROGEO)

2020 ◽  
Author(s):  
Elaine Pimentel
Keyword(s):  
Projective Geometry ◽  
Automated Deduction ◽  
First Order ◽  
Systematic Procedure ◽  
Proof Systems ◽  
Conservative Extensions

We plan to study the problem of finding conservative extensions of first order logics. In this project we intend to establish a systematic procedure for adding geometric theories in both intuitionistic and classical logics, as well as to extend this procedure to bipolar axioms, a generalization of the set of geometric axioms. This way, we obtain proof systems for several mathematical theories, such as lattices, algebra and projective geometry, being able to reason about such theories using automated deduction.

scholarly journals Reasoning with Inconsistent Possibilistic Ontologies by Applying Argument Accrual

2017 ◽  
Vol 17 (02) ◽  
pp. e16
Author(s):  
Sergio Alejandro Gómez
Keyword(s):  
Logic Programming ◽  
Description Logic ◽  
Logic Programs ◽  
Argumentation Framework ◽  
Abstract Argumentation ◽  
Possibilistic Logic ◽  
Grounded Semantics

We present an approach for performing instance checking in possibilistic description logic programming ontologies by accruing arguments that support the membership of individuals to concepts. Ontologies are interpreted as possibilistic logic programs where accruals of arguments as regarded as vertexes in an abstract argumentation framework. A suitable attack relation between accruals is defined. We present a reasoning framework with a case study and a Java-based implementation for enacting the proposed approach that is capable of reasoning under Dung’s grounded semantics.

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