The purpose of this note is to suggest an alternative explanation of the relationship between predicate logics with equality and linear logic. The explanation given by Girard resorts to so called exponentials, which are believed to extract from a linear formula A its classical content !A and ?A. Thus, Girard gives a top-down explanation of the relationship between linear and classical logics: t...

We introduce a new formal logic, called equality propositional logic. It has two basic connectives, $boldsymbol{wedge}$ (conjunction) and $equiv$ (equivalence). Moreover, the $Rightarrow$ (implication) connective can be derived as $ARightarrow B:=(Aboldsymbol{wedge}B)equiv A$. We formulate the equality propositional logic and demonstrate that the resulting logic has reasonable properties such a...

SpeechLe1! is a module of an experimental speech recognition system. The main features of this system are the rule-based approach for the acousticphonetic detection, the incorporation of Fuzzy Logic to handle uncertain decisions, and an overall top-down recognition strategy. The task of SpeechLez is to set up a phonotactical network describing the words of a given vocabulary with common variati...

We present a simple, yet general top-down query answering procedure for normal logic programs over lattices and bilattices, where functions may appear in the rule bodies. Its interest relies on the fact that many approaches to paraconsistency and uncertainty in logic programs with or without non-monotonic negation are based on bilattices or lattices, respectively.

We present a novel approach to non-monotonic ILP and its implementation called tal (Top-directed Abductive Learning). tal overcomes some of the completeness problems of ILP systems based on Inverse Entailment and is the first top-down ILP system that allows background theories and hypotheses to be normal logic programs. The approach relies on mapping an ILP problem into an equivalent ALP one. T...