In this paper, we investigate the extraction of fuzzy rules from data tables based on possibility theory. A possibilistic decision language is used to represent the extracted fuzzy rules. The algorithm for rule extraction is presented and the complexity analysis is carried out. Since the results of the rule induction process strongly depend on the representation language, we also discuss some a...

We specify an information flow analysis for a simple imperative language, using a Hoare-like logic. The logic facilitates static checking of a larger class of programs than can be checked by extant type-based approaches in which a program is deemed insecure when it contains an insecure subprogram. The logic is based on an abstract interpretation of program traces that makes independence between...

In Apt (1998) we provided a proof theoretic account of constraint programming. Here we show how it can be used to analyse Boolean constraints. More precisely, we show here how a Boolean constraint solver based on the look-ahead search strategy can be defined in a purely logical way. To this end we characterize arc consistency for Boolean constraints by proof theoretic means. As a byproduct we c...

A Formal Logical Analysis of Causal Relations Summary Causal relations of various kinds are a pervasive feature of human language and theorising about the world. Despite this, the specification of a satisfactory general analysis of causal relations has long proved difficult. The research described in this thesis is an attempt to provide a formal logical theory of causal relations, in a broad se...

This report contains the description of the main methods, implemented in ASTRA 3.0, to analyse coherent andnon-coherent fault trees. ASTRA 3.0 is fully based on the Binary Decision Diagrams (BDD) approach. In thecase of non-coherent fault trees ASTRA 3.0 dynamically assigns to each node of the graph a label that identifiesthe type of the associated variable in order to drive the...

In this paper we prove general logical metatheorems which state that for large classes of theorems and proofs in (nonlinear) functional analysis it is possible to extract from the proofs effective bounds which depend only on very sparse local bounds on certain parameters. This means that the bounds are uniform for all parameters meeting these weak local boundedness conditions. The results vastl...

Sets of “positive” and “negative” points (observations) in n-dimensional discrete space given along with their non-negative integer multiplicities are analyzed from the perspective of the Logical Analysis of Data (LAD). A set of observations satisfying upper and/or lower bounds imposed on certain components is called a positive pattern if it contains some positive observations and no negative o...