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String-based Multi-adjoint Lattices for Tracing Fuzzy Logic Computations

Classically, most programming languages use in a predefined way the notion of «string» as an standard data structure for a comfortable management of arbitrary sequences of characters. However, in this paper we assign a different role to this concept: here we are concerned with fuzzy logic programming, a somehow recent paradigm trying to introduce fuzzy logic into logic programming. In this setting, the mathematical concept of multi-adjoint lattice has been successfully exploited into the so-called Multi-adjoint Logic Programming approach, MALP in brief, for modeling flexible notions of truth-degrees beyond the simpler case of true and false. Our main goal points out not only our formal proof verifying that stringbased lattices accomplish with the so-called multi-adjoint property (as well as its Cartesian product with similar structures), but also its correspondence with interesting debugging tasks into the FLOPER system (from «Fuzzy LOgic Programming Environment for Research») developed in our research group.

A Declarative Debugger for Concurrent Erlang Programs

Erlang is a concurrent language with features such as actor model concurrency, no shared memory, message passing communication, high scalability and availability. However, the development of concurrent programs is a complex and error prone task. In this paper we present a declarative debugging approach for concurrent Erlang programs. Our debugger asks questions about the validity of transitions between the different points of the program that involve message passing and/or process creation. The answers, which represent the intended behavior of the program, are compared with the transitions obtained in an actual execution of the program. The differences allow us to detect program errors and to point out the pieces of source code responsible for the bugs. In order to represent the computations we present a semantic calculus for concurrent Core Erlang programs. The debugger uses the proof trees in this calculus as debugging trees used for selecting the questions asked to the user. The relation between the debugging trees and the semantic calculus allows us to establish the soundness of the approach. The theoretical ideas have been implemented in a debugger prototype.