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

Extending FuzAtAnalyzer to approach the management of classical negation

FuzAtAnalyzer was conceived as a Java framework which goes beyond of classical tools in formal concept analysis. Specifically, it successfully incorporated the management of uncertainty by means of methods and tools from the area of fuzzy formal concept analysis. One limitation of formal concept analysis is that they only consider the presence of properties in the objects (positive attributes) as much in fuzzy as in crisp case. In this paper, a first step in the incorporation of negations is presented. Our aim is the treatment of the absence of properties (negative attributes). Specifically, we extend the framework by including specific tools for mining knowledge combining crisp positive and negative attributes.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Truth-Valued-Flow Inference (TVFI) and its applications in approximate reasoning

The framework of the theory of Truth-valued-flow Inference (TVFI) is introduced. Even though there are dozens of papers presented on fuzzy reasoning, we think it is still needed to explore a rather unified fuzzy reasoning theory which has the following two features: (1) it is simplified enough to be executed feasibly and easily; and (2) it is well structural and well consistent enough that it can be built into a strict mathematical theory and is consistent with the theory proposed by L.A. Zadeh. TVFI is one of the fuzzy reasoning theories that satisfies the above two features. It presents inference by the form of networks, and naturally views inference as a process of truth values flowing among propositions

On the incorporation of interval-valued fuzzy sets into the Bousi-Prolog system: declarative semantics, implementation and applications

In this paper we analyse the benefits of incorporating interval-valued fuzzy sets into the Bousi-Prolog system. A syntax, declarative semantics and im- plementation for this extension is presented and formalised. We show, by using potential applications, that fuzzy logic programming frameworks enhanced with them can correctly work together with lexical resources and ontologies in order to improve their capabilities for knowledge representation and reasoning

Fuzzy inequational logic

We present a logic for reasoning about graded inequalities which generalizes the ordinary inequational logic used in universal algebra. The logic deals with atomic predicate formulas of the form of inequalities between terms and formalizes their semantic entailment and provability in graded setting which allows to draw partially true conclusions from partially true assumptions. We follow the Pavelka approach and define general degrees of semantic entailment and provability using complete residuated lattices as structures of truth degrees. We prove the logic is Pavelka-style complete. Furthermore, we present a logic for reasoning about graded if-then rules which is obtained as particular case of the general result

Dual Logic Concepts based on Mathematical Morphology in Stratified Institutions: Applications to Spatial Reasoning

Several logical operators are defined as dual pairs, in different types of logics. Such dual pairs of operators also occur in other algebraic theories, such as mathematical morphology. Based on this observation, this paper proposes to define, at the abstract level of institutions, a pair of abstract dual and logical operators as morphological erosion and dilation. Standard quantifiers and modalities are then derived from these two abstract logical operators. These operators are studied both on sets of states and sets of models. To cope with the lack of explicit set of states in institutions, the proposed abstract logical dual operators are defined in an extension of institutions, the stratified institutions, which take into account the notion of open sentences, the satisfaction of which is parametrized by sets of states. A hint on the potential interest of the proposed framework for spatial reasoning is also provided.Comment: 36 page