Multi-adjoint logic program generalise monotonic logic programs introduced in [1] in that simulta... more Multi-adjoint logic program generalise monotonic logic programs introduced in [1] in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed. In this work, a procedural semantics is given for the paradigm of multi-adjoint logic programming and completeness theorems are proved.
Generalisation of the foundational basis for many-valued logic programming builds upon generalise... more Generalisation of the foundational basis for many-valued logic programming builds upon generalised terms in the form of powersets of terms. A categorical approach involving set and term functors as monads allows for a study of monad compositions that provide variable substitutions and compositions thereof. In this paper, substitutions and unifiers appear as constructs in Kleisli categories related to particular composed powerset term monads.
Abstract Reduction strategies are introduced for the future fragment of a temporal propositional ... more Abstract Reduction strategies are introduced for the future fragment of a temporal propositional logic on linear discrete time, named FNext. These reductions are based on the information collected from the syntactic structure of the formula, which allows the development of efficient strategies to decrease the size of temporal propositional formulas, viz. new criteria to detect the validity or unsatisfiability of subformulas, and a strong generalisation of the pure literal rule.
Fuzzy logic programming represents a flexible and powerful declarative paradigm amalgamating fuzz... more Fuzzy logic programming represents a flexible and powerful declarative paradigm amalgamating fuzzy logic and logic programming, for which there exists different promising approaches described in the literature. In this paper we propose an improved fuzzy query answering procedure for the so called multi-adjoint logic programming approach, which avoids the re-evaluation of goals and the generation of useless computations thanks to the combined use of tabulation with thresholding techniques.
We use the formal model for similarity-based fuzzy unification in multi-adjoint logic programs to... more We use the formal model for similarity-based fuzzy unification in multi-adjoint logic programs to provide new tools for flexible querying. Our approach is based on a general framework for logic programming, which gives a formal model of fuzzy logic programming extended by fuzzy similarities and axioms of first-order logic with equality.
Abstract Many-valued logic programming with generalised terms requires an extended notion of unif... more Abstract Many-valued logic programming with generalised terms requires an extended notion of unification in order to handle powersets of terms. In this paper we present substitutions and unifiers in a categorical framework based on powersets of terms as monads. We build upon developments for monad compositions initiated in [4].
Several fuzzifications of formal concept analysis have been proposed to deal with uncertain infor... more Several fuzzifications of formal concept analysis have been proposed to deal with uncertain information. In this paper, we focus on concept lattices under a multi-adjoint paradigm, which enriches the language providing greater flexibility to the user in that he/she can choose from a number of different connectives.
Composing various powerset functors with the term monad gives rise to the concept of generalized ... more Composing various powerset functors with the term monad gives rise to the concept of generalized terms. This in turn provides a technique for handling many-valued sets of terms in a framework of variable substitutions, thus being the prerequisite for categorical unification in many-valued logic programming using an extended notion of terms.
Abstract. Residuated Logic Programs allow to capture a spate of different semantics dealing with ... more Abstract. Residuated Logic Programs allow to capture a spate of different semantics dealing with uncertainty and vagueness. In this work we provide a tabulation goal-oriented query procedure, and show that our tabulation query procedure terminates if and only if the sequence of iterations of the immediate consequences operator reaches the least fixpoint after only finitely-many steps.
We introduce a sufficient condition which guarantees the existence of stable models for a normal ... more We introduce a sufficient condition which guarantees the existence of stable models for a normal residuated logic program interpreted on the truth-space [0, 1] n. Specifically, the continuity of the connectives involved in the program ensures the existence of stable models. Then, we study conditions which guarantee the uniqueness of stable models in the particular case of the product t-norm, its residuated implication and the standard negation.
Unlike monotone single-valued functions, multivalued mappings may have zero, one, or (possibly in... more Unlike monotone single-valued functions, multivalued mappings may have zero, one, or (possibly infinitely) many minimal fixed-points. The contribution of this work is twofold. First, we overview and investigate the existence and computation of minimal fixed-points of multivalued mappings, whose domain is a complete lattice and whose range is its power set. Second, we show how these results are applied to a general form of logic programs, where the truth space is a complete lattice.
Logic programming has been used as a natural framework to automate deduction in the logic of orde... more Logic programming has been used as a natural framework to automate deduction in the logic of order-of-magnitude reasoning. Specifically, we introduce a Prolog implementation of the Rasiowa–Sikorski proof system associated with the relational translation Re (OM) of the multi-modal logic of order-of-magnitude qualitative reasoning OM.
Abstract. In Formal Concept Analysis, attribute reduction is a important step in order to reduce ... more Abstract. In Formal Concept Analysis, attribute reduction is a important step in order to reduce the complexity of the computation of the concept lattice. This reduction is more complex in fuzzy environments. In this paper, we will present a first approximation to reduce the set of attributes in the multi-adjoint concept lattice.
Abstract In this paper we continue analyzing the introduction of negation into the framework of r... more Abstract In this paper we continue analyzing the introduction of negation into the framework of residuated logic programming [18],[19]; specifically, we focus on extended programs, in which strong negation is introduced.
A neural approach to propositional multi-adjoint logic programming was recently introduced. In th... more A neural approach to propositional multi-adjoint logic programming was recently introduced. In this paper we extend the neural approach to multiadjoint deduction and, furthermore, modify it to cope with abductive multi-adjoint reasoning, where adaptations of the uncertainty factor in a knowledge base are carried out automatically so that a number of given observations can be adequately explained.
In this work, we generalize previous constructions of fuzzy set categories, introduced in [1], by... more In this work, we generalize previous constructions of fuzzy set categories, introduced in [1], by considering L-fuzzy sets in which the values of the characteristic functions run on a completely distributive lattice, rather than in the unit real interval. Later, these L-fuzzy sets are used to define the L-fuzzy categories, which are proven to be rational.
We briefly overview the most recent improvements we have incorporated to the existent implementat... more We briefly overview the most recent improvements we have incorporated to the existent implementations of the TAS methodology, the simplified Δ-tree representation of formulas in negation normal form. This new representation allows for a better description of the reduction strategies, in that considers only those occurrences of literals which are relevant for the satisfiability of the input formula.
Multi-adjoint logic program generalise monotonic logic programs introduced in [1] in that simulta... more Multi-adjoint logic program generalise monotonic logic programs introduced in [1] in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed. In this work, a procedural semantics is given for the paradigm of multi-adjoint logic programming and completeness theorems are proved.
Generalisation of the foundational basis for many-valued logic programming builds upon generalise... more Generalisation of the foundational basis for many-valued logic programming builds upon generalised terms in the form of powersets of terms. A categorical approach involving set and term functors as monads allows for a study of monad compositions that provide variable substitutions and compositions thereof. In this paper, substitutions and unifiers appear as constructs in Kleisli categories related to particular composed powerset term monads.
Abstract Reduction strategies are introduced for the future fragment of a temporal propositional ... more Abstract Reduction strategies are introduced for the future fragment of a temporal propositional logic on linear discrete time, named FNext. These reductions are based on the information collected from the syntactic structure of the formula, which allows the development of efficient strategies to decrease the size of temporal propositional formulas, viz. new criteria to detect the validity or unsatisfiability of subformulas, and a strong generalisation of the pure literal rule.
Fuzzy logic programming represents a flexible and powerful declarative paradigm amalgamating fuzz... more Fuzzy logic programming represents a flexible and powerful declarative paradigm amalgamating fuzzy logic and logic programming, for which there exists different promising approaches described in the literature. In this paper we propose an improved fuzzy query answering procedure for the so called multi-adjoint logic programming approach, which avoids the re-evaluation of goals and the generation of useless computations thanks to the combined use of tabulation with thresholding techniques.
We use the formal model for similarity-based fuzzy unification in multi-adjoint logic programs to... more We use the formal model for similarity-based fuzzy unification in multi-adjoint logic programs to provide new tools for flexible querying. Our approach is based on a general framework for logic programming, which gives a formal model of fuzzy logic programming extended by fuzzy similarities and axioms of first-order logic with equality.
Abstract Many-valued logic programming with generalised terms requires an extended notion of unif... more Abstract Many-valued logic programming with generalised terms requires an extended notion of unification in order to handle powersets of terms. In this paper we present substitutions and unifiers in a categorical framework based on powersets of terms as monads. We build upon developments for monad compositions initiated in [4].
Several fuzzifications of formal concept analysis have been proposed to deal with uncertain infor... more Several fuzzifications of formal concept analysis have been proposed to deal with uncertain information. In this paper, we focus on concept lattices under a multi-adjoint paradigm, which enriches the language providing greater flexibility to the user in that he/she can choose from a number of different connectives.
Composing various powerset functors with the term monad gives rise to the concept of generalized ... more Composing various powerset functors with the term monad gives rise to the concept of generalized terms. This in turn provides a technique for handling many-valued sets of terms in a framework of variable substitutions, thus being the prerequisite for categorical unification in many-valued logic programming using an extended notion of terms.
Abstract. Residuated Logic Programs allow to capture a spate of different semantics dealing with ... more Abstract. Residuated Logic Programs allow to capture a spate of different semantics dealing with uncertainty and vagueness. In this work we provide a tabulation goal-oriented query procedure, and show that our tabulation query procedure terminates if and only if the sequence of iterations of the immediate consequences operator reaches the least fixpoint after only finitely-many steps.
We introduce a sufficient condition which guarantees the existence of stable models for a normal ... more We introduce a sufficient condition which guarantees the existence of stable models for a normal residuated logic program interpreted on the truth-space [0, 1] n. Specifically, the continuity of the connectives involved in the program ensures the existence of stable models. Then, we study conditions which guarantee the uniqueness of stable models in the particular case of the product t-norm, its residuated implication and the standard negation.
Unlike monotone single-valued functions, multivalued mappings may have zero, one, or (possibly in... more Unlike monotone single-valued functions, multivalued mappings may have zero, one, or (possibly infinitely) many minimal fixed-points. The contribution of this work is twofold. First, we overview and investigate the existence and computation of minimal fixed-points of multivalued mappings, whose domain is a complete lattice and whose range is its power set. Second, we show how these results are applied to a general form of logic programs, where the truth space is a complete lattice.
Logic programming has been used as a natural framework to automate deduction in the logic of orde... more Logic programming has been used as a natural framework to automate deduction in the logic of order-of-magnitude reasoning. Specifically, we introduce a Prolog implementation of the Rasiowa–Sikorski proof system associated with the relational translation Re (OM) of the multi-modal logic of order-of-magnitude qualitative reasoning OM.
Abstract. In Formal Concept Analysis, attribute reduction is a important step in order to reduce ... more Abstract. In Formal Concept Analysis, attribute reduction is a important step in order to reduce the complexity of the computation of the concept lattice. This reduction is more complex in fuzzy environments. In this paper, we will present a first approximation to reduce the set of attributes in the multi-adjoint concept lattice.
Abstract In this paper we continue analyzing the introduction of negation into the framework of r... more Abstract In this paper we continue analyzing the introduction of negation into the framework of residuated logic programming [18],[19]; specifically, we focus on extended programs, in which strong negation is introduced.
A neural approach to propositional multi-adjoint logic programming was recently introduced. In th... more A neural approach to propositional multi-adjoint logic programming was recently introduced. In this paper we extend the neural approach to multiadjoint deduction and, furthermore, modify it to cope with abductive multi-adjoint reasoning, where adaptations of the uncertainty factor in a knowledge base are carried out automatically so that a number of given observations can be adequately explained.
In this work, we generalize previous constructions of fuzzy set categories, introduced in [1], by... more In this work, we generalize previous constructions of fuzzy set categories, introduced in [1], by considering L-fuzzy sets in which the values of the characteristic functions run on a completely distributive lattice, rather than in the unit real interval. Later, these L-fuzzy sets are used to define the L-fuzzy categories, which are proven to be rational.
We briefly overview the most recent improvements we have incorporated to the existent implementat... more We briefly overview the most recent improvements we have incorporated to the existent implementations of the TAS methodology, the simplified Δ-tree representation of formulas in negation normal form. This new representation allows for a better description of the reduction strategies, in that considers only those occurrences of literals which are relevant for the satisfiability of the input formula.
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Papers by Manuel Ojeda-Aciego