40,210 research outputs found
Resolution in Linguistic Propositional Logic based on Linear Symmetrical Hedge Algebra
The paper introduces a propositional linguistic logic that serves as the
basis for automated uncertain reasoning with linguistic information. First, we
build a linguistic logic system with truth value domain based on a linear
symmetrical hedge algebra. Then, we consider G\"{o}del's t-norm and t-conorm to
define the logical connectives for our logic. Next, we present a resolution
inference rule, in which two clauses having contradictory linguistic truth
values can be resolved. We also give the concept of reliability in order to
capture the approximative nature of the resolution inference rule. Finally, we
propose a resolution procedure with the maximal reliability.Comment: KSE 2013 conferenc
Many-valued logics. A mathematical and computational introduction.
2nd edition. Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values. This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic—as well as other non-classical logics—is of no avail. Indeed, originally motivated by philosophical concerns, these logics soon proved relevant for a plethora of applications ranging from switching theory to cognitive modeling, and they are today in more demand than ever, due to the realization that inconsistency and vagueness in knowledge bases and information processes are not only inevitable and acceptable, but also perhaps welcome.
The main modern applications of (any) logic are to be found in the digital computer, and we thus require the practical knowledge how to computerize—which also means automate—decisions (i.e. reasoning) in many-valued logics. This, in turn, necessitates a mathematical foundation for these logics. This book provides both these mathematical foundation and practical knowledge in a rigorous, yet accessible, text, while at the same time situating these logics in the context of the satisfiability problem (SAT) and automated deduction.
The main text is complemented with a large selection of exercises, a plus for the reader wishing to not only learn about, but also do something with, many-valued logics
A Fuzzy Logic Programming Environment for Managing Similarity and Truth Degrees
FASILL (acronym of "Fuzzy Aggregators and Similarity Into a Logic Language")
is a fuzzy logic programming language with implicit/explicit truth degree
annotations, a great variety of connectives and unification by similarity.
FASILL integrates and extends features coming from MALP (Multi-Adjoint Logic
Programming, a fuzzy logic language with explicitly annotated rules) and
Bousi~Prolog (which uses a weak unification algorithm and is well suited for
flexible query answering). Hence, it properly manages similarity and truth
degrees in a single framework combining the expressive benefits of both
languages. This paper presents the main features and implementations details of
FASILL. Along the paper we describe its syntax and operational semantics and we
give clues of the implementation of the lattice module and the similarity
module, two of the main building blocks of the new programming environment
which enriches the FLOPER system developed in our research group.Comment: In Proceedings PROLE 2014, arXiv:1501.0169
FURY: Fuzzy unification and resolution based on edit distance
We present a theoretically founded framework for fuzzy
unification and resolution based on edit distance over trees.
Our framework extends classical unification and resolution
conservatively. We prove important properties of the framework
and develop the FURY system, which implements the
framework efficiently using dynamic programming. We
evaluate the framework and system on a large problem in
the bioinformatics domain, that of detecting typographical
errors in an enzyme name databas
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