Finite-valued Lukasiewicz modal logic is PSPACE-complete
Publication Type:
Conference PaperSource:
Twenty-second International Joint Conference on Artificial Intelligence (IJCAI 2011), Barcelona, p.774 - 779 (2011)ISBN:
978-1-57735-516-8Abstract:
It is well-known that satisfiability (and hence validity) in the minimal classical modal logic is a PSPACE-complete problem. In this paper we consider the satisfiability and validity problems (here they are not dual, although mutually reducible) for the minimal modal logic over a finite Lukasiewicz chain, and show that they also are PSPACE-complete. This result is also true when adding either the Delta operator or truth constants in the language, i.e. in all these cases it is PSPACE- complete.
On Similarities in Fuzzy Description Logics
Publication Type:
Conference PaperSource:
Logic, Algebra and Truth Degrees 2010, Volume 502, Praga, p.44-49 (2010)Keywords:
fuzzy description logics; similaritiesAbstract:
In this paper we explore the possibility of introducing the equality
symbol in the languages of Fuzzy Description Logics (FDLs)
interpreted as a similarity relation. In the talk we will present a
state of the art concerning the notion of similarity in some fields
of artificial intelligence, and we analyze some variants of the
languages for the FDLs introduced in [GaArEs10]. The goal is
twofold: dealing with attribute-value representations at the domain
objects level, and integrating the treatment of similarities inside
the description languages and their corresponding knowledge bases.
Decidability of a Description Logic over infinite-valued Product Logic
Publication Type:
Conference PaperSource:
12th Conference on Principles of Knowledge Representation and Reasoning, KR 2010, AAAI Press, Toronto (Canada), p.203-213 (2010)Abstract:
This paper proves that validity and satisfiability of
assertions in the Fuzzy Description Logic based on infinite-valued
Product Logic with universal and existential quantifiers (which are
non-interdefinable) is decidable when we only consider quasi-witnessed
interpretations. We prove that this restriction is neither necessary for the validity
problem (i.e., the validity of assertions in the Fuzzy Description Logic
based on infinite-valued Product Logic is decidable) nor for the
positive satisfiability problem, because quasi-witnessed interpretations
are particularly adequate for the infinite-valued Product Logic.
We give an algorithm that reduces the problem of validity (and
satisfiability) of assertions in our Fuzzy Description Logic (restricted to
quasi-witnessed interpretations) to a semantic consequence problem, with
finite number of hypothesis, on infinite-valued propositional Product
Logic.
From Classical Description Logic to n-graded Fuzzy Description logics
Fuzzy Description Logics and t-norm based Fuzzy Logics
Publication Type:
Journal ArticleSource:
International Journal of Approximate reasoning, Elsevier, Volume 51, Issue 6, p.632 -- 655 (2010)Keywords:
Description Logics; Fuzzy Description Logics; Many-valued Logics; Propositional and Predicate t-norm based Fuzzy Logics; Truth-constantsReceived 22 May 2009Abstract:
Description Logics (DLs) are knowledge representation languages built on the basis of classical logic. DLs allow the creation of knowledge bases and provide ways to reason on the contents of these bases. Fuzzy Description Logics (FDLs) are natural extensions of DLs for
dealing with vague concepts, commonly present in real applications. Ha?jek proposed to
deal with FDLs taking as basis t-norm based fuzzy logics with the aim of enriching the
expressive possibilities in FDLs and to capitalize on recent developments in the field of
Mathematical Fuzzy Logic. From this perspective we define a family of description lan-
guages, denoted by
ALC
On Triangular Norm based Fuzzy Description Logics
Publication Type:
Conference PaperSource:
IFSA-EUSFLAT, Calouste Gulbekian Foundation, 20-24 July 2009. Lisbon, Portugal, p.891-896 (2009)ISBN:
978-989-95079-6-8Keywords:
Description Logics; Fuzzy Description Logics; t-norm based fuzzy logics; Truth-constants; Involutive negationAbstract:
Description Logics (DLs) are knowledge representation languages useful to represent concepts and roles. Fuzzy Description Logics (FDLs) incorporate both vague concepts and vague roles
modeling them as fuzzy sets and fuzzy relations respectively.
In the present paper, following ideas from H\'ajek, we propose the use of t-norm based (fuzzy) logics with truth constants in the language as logics underlying the fuzzy description language. We introduce the
languages ALC_L*(Al[S]) and ALC_L*_(Al[S]) as an adequate syntactical counterpart of some semantic calculi given in different works dealing with FDLs.
