322 research outputs found
Lukasiewicz mu-Calculus
We consider state-based systems modelled as coalgebras whose type incorporates branching, and show that by suitably adapting the definition of coalgebraic bisimulation, one obtains a general and uniform account of the linear-time behaviour of a state in such a coalgebra. By moving away from a boolean universe of truth values, our approach can measure the extent to which a state in a system with branching is able to exhibit a particular linear-time behaviour. This instantiates to measuring the probability of a specific behaviour occurring in a probabilistic system, or measuring the minimal cost of exhibiting a specific behaviour in the case of weighted computations
Modeling multi-valued biological interaction networks using Fuzzy Answer Set Programming
Fuzzy Answer Set Programming (FASP) is an extension of the popular Answer Set Programming (ASP) paradigm that allows for modeling and solving combinatorial search problems in continuous domains. The recent development of practical solvers for FASP has enabled its applicability to real-world problems. In this paper, we investigate the application of FASP in modeling the dynamics of Gene Regulatory Networks (GRNs). A commonly used simplifying assumption to model the dynamics of GRNs is to assume only Boolean levels of activation of each node. Our work extends this Boolean network formalism by allowing multi-valued activation levels. We show how FASP can be used to model the dynamics of such networks. We experimentally assess the efficiency of our method using real biological networks found in the literature, as well as on randomly-generated synthetic networks. The experiments demonstrate the applicability and usefulness of our proposed method to find network attractors
On triangular norms and uninorms definable in ŁΠ12
AbstractIn this paper, we investigate the definability of classes of t-norms and uninorms in the logic ŁΠ12. In particular we provide a complete characterization of definable continuous t-norms, weak nilpotent minimum t-norms, conjunctive uninorms continuous on [0,1), and idempotent conjunctive uninorms, and give both positive and negative results concerning definability of left-continuous t-norms (and uninorms). We show that the class of definable uninorms is closed under construction methods as annihilation, rotation and rotation–annihilation. Moreover, we prove that every logic based on a definable uninorm is in PSPACE, and that any finitely axiomatizable logic based on a class of definable uninorms is decidable. Finally we show that the Uninorm Mingle Logic (UML) and the Basic Uninorm Logic (BUL) are finitely strongly standard complete w.r.t. the related class of definable left-continuous conjunctive uninorms
I can get some satisfaction: Fuzzy ontologies for partial agreements in blockchain smart contracts
This paper proposes a novel extension of blockchain systems with fuzzy ontologies. The main advantage is to let the users have flexible restrictions, represented using fuzzy sets, and to develop smart contracts where there is a partial agreement among the involved parts. We propose a general architecture based on four fuzzy ontologies and a process to develop and run the smart contracts, based on a reduction to a well-known fuzzy ontology reasoning task (Best Satisfiability Degree). We also investigate different operators to compute Pareto-optimal solutions and implement our approach in the Ethereum blockchain
Fuzzy ontology representation using OWL 2
AbstractThe need to deal with vague information in Semantic Web languages is rising in importance and, thus, calls for a standard way to represent such information. We may address this issue by either extending current Semantic Web languages to cope with vagueness, or by providing a procedure to represent such information within current standard languages and tools. In this work, we follow the latter approach, by identifying the syntactic differences that a fuzzy ontology language has to cope with, and by proposing a concrete methodology to represent fuzzy ontologies using OWL 2 annotation properties. We also report on some prototypical implementations: a plug-in to edit fuzzy ontologies using OWL 2 annotations and some parsers that translate fuzzy ontologies represented using our methodology into the languages supported by some reasoners
Sorites, curry and suitable models
In this paper we present two new approaches for dealing with semantic paradoxes and soritical predicates based on fuzzy logic. We show that both of them have conceptual advantages over the more traditional Łukasiewicz approach, and that the second one even avoids standard proofs of w-inconsistency.Fil: Da Re, Bruno. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Filosóficas. - Sociedad Argentina de Análisis Filosófico. Instituto de Investigaciones Filosóficas; ArgentinaFil: Teijeiro, Paula. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Filosóficas. - Sociedad Argentina de Análisis Filosófico. Instituto de Investigaciones Filosóficas; Argentin
Foundations of Reasoning with Uncertainty via Real-valued Logics
Real-valued logics underlie an increasing number of neuro-symbolic
approaches, though typically their logical inference capabilities are
characterized only qualitatively. We provide foundations for establishing the
correctness and power of such systems. For the first time, we give a sound and
complete axiomatization for a broad class containing all the common real-valued
logics. This axiomatization allows us to derive exactly what information can be
inferred about the combinations of real values of a collection of formulas
given information about the combinations of real values of several other
collections of formulas. We then extend the axiomatization to deal with
weighted subformulas. Finally, we give a decision procedure based on linear
programming for deciding, under certain natural assumptions, whether a set of
our sentences logically implies another of our sentences.Comment: 9 pages (incl. references), 9 pages supplementary. In submission to
NeurIPS 202
Weighted logics for artificial intelligence : an introductory discussion
International audienceBefore presenting the contents of the special issue, we propose a structured introductory overview of a landscape of the weighted logics (in a general sense) that can be found in the Artificial Intelligence literature, highlighting their fundamental differences and their application areas
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