Teresa Alsinet

Improved exact solvers for weighted Max-SAT

We present two new branch and bound weighted Max-SAT solvers (Lazy and Lazy*) which incorporate original data structures and inference rules, and a lower bound of better quality.

Argument-Based expansion operators in possibilistic defeasible logic programming: characterization and logical properties

Possibilistic Defeasible Logic Programming (P-DeLP) is a logic programming language which combines features from argumentation theory and logic programming, incorporating as well the treatment of possibilistic uncertainty and fuzzy knowledge at object-language level. Defeasible argumentation in general and P-DeLP in particular provide a way of modelling non-monotonic inference. From a logical viewpoint, capturing defeasible inference relationships for modelling argument and warrant is particularly important, as well as the study of their logical properties. This paper analyzes two non-monotonic operators for P-DeLP which model the expansion of a given program

A Max-SAT Solver with Lazy Data Structures

\mathcal{P}

A Proof Procedure for Possibilistic Logic Programming with Fuzzy Constants

by adding new weighed facts associated with argument conclusions and warranted literals, resp. Different logical properties for the proposed expansion operators are studied and contrasted with a traditional SLD-based Horn logic. We will show that this analysis provides useful comparison criteria that can be extended and applied to other argumentation frameworks.

Different models of fuzzy logic programming with fuzzy unification (towards a revision of fuzzy databases)

We present a new branch and bound algorithm for Max-SAT which incorporates original lazy data structures, a new variable selection heuristics and a lower bound of better quality. We provide experimental evidence that our solver outperforms some of the best performing Max-SAT solvers on a wide range of instances.

Using Answer Set Programming for an Scalable Implementation of Defeasible Argumentation

In a recent work we defined a possibilistic logic programming language, called PGL+, dealing with fuzzy propositions and with a fuzzy unification mechanism. The proof system, modus ponens-style, was shown to be complete when restricted to a class of Horn clauses satisfying two types of constraints. In this paper we complete the definition of the logic programming system. In particular, we first formalize a notion of PGL+ program and discuss the two types of constraints (called modularity and context constraints) we argue they must satisfy; second, we extend the PGL+ calculus with a chaining and fusion mechanism whose application ensures the fulfillment of the modularity constraint; and finally, we define an efficient (as much as possible) proof procedure oriented to goals which is complete for PGL+ programs satisfying the context constraint.

Maximal ideal recursive semantics for defeasible argumentation

The aim of the paper is to show relationships between different formalisms for handling uncertainty in logic programming, knowledge based systems and deductive databases. Namely, we show that our model of fuzzy logic programming has the same expressive power as annotated logic programs with restricted continuous semantics. Features of fuzzy unification are achieved by extending the rule base by axioms of equality with fuzzy similarities. This induces a new fuzzy relational algebra. Our procedural semantics enables us to estimate truth values of the answers during the computation. Using this, we introduce a model with threshold computation and another for finding the best answer with prescribed precision tolerance.

Minimal and Redundant SAT Encodings for the All-Interval-Series Problem

In previous works, a recursive warrant semantics for Defeasible Logic Programming extended with levels of possibilistic uncertainty for defeasible rules was introduced. The resulting argumentation framework, called RP-DeLP, is based on a general notion of collective (non-binary) conflict among arguments allowing to ensure direct and indirect consistency properties with respect to the strict knowledge. In this paper we propose an efficient and scalable implementation of an interpreter for RP-DeLP using Answer Set Programming (ASP) encodings for the two main queries of the system: looking for valid arguments and finding collective conflicts among arguments. We perform an experimental evaluation of our ASP approach and we compare the results with a previously proposed SAT based approach. The results show that with ASP we are able to scale up to bigger problem instances.

Weighted argumentation for analysis of discussions in Twitter

In a previous work we defined a recursive warrant semantics for Defeasible Logic Programming extended with levels of possibilistic uncertainty for defeasible rules. The resulting argumentation framework, called RP-DeLP, is based on a general notion of collective (non-binary) conflict among arguments allowing to ensure direct and indirect consistency properties with respect to the strict knowledge. An output of an RP-DeLP program is a pair of sets of warranted and blocked conclusions (literals), all of them recursively based on warranted conclusions but, while warranted conclusions do not generate any conflict, blocked conclusions do. An RP-DeLP program may have multiple outputs in case of circular definitions of conflicts among arguments. In this paper we tackle the problem of which output one should consider for an RP-DeLP program with multiple outputs. To this end we define the maximal ideal output of an RPDeLP program as the set of conclusions which are ultimately warranted and we present an algorithm for computing them in polynomial space and with an upper bound on complexity equal to PNP.

On the implementation of a Fuzzy DL Solver over Infinite-Valued Product Logic with SMT Solvers

The SAT encodings defined so far for the all-interval-series (ais) problem are very hard for local search but rather easy for systematic algorithms. We define different SAT encodings for the ais problem and provide experimental evidence that this problem can be efficiently solved with local search methods if one chooses a suitable SAT encoding.