Investigated are possibilistic distributions taking as their values sequences from the infinite Cartesian product of identical copies of a fixed finite subset of the unit interval of real numbers. Uniform and lexicographic partial orderings on the space of these sequences are defined and the related complete lattices introduced. Lattice-valued entropy function is defined in the common pattern f...

In this paper, we consider one of the most fundamental results on periodicity of words, namely the critical factorization theorem. Given a word w and nonempty words u, v satisfying w = uv, the minimal local period associated to the factorization (u, v) is the length of the shortest square at position |u| − 1. The critical factorization theorem shows that for any word, there is always a factoriz...

The lexicographically-ordered CSP (“lexicographic CSP” or “LO-CSP” for short) combines a simple representation of preferences with the feasibility constraints of ordinary CSPs. Preferences are defined by a total ordering across all assignments, such that a change in assignment to a given variable is more important than any change in assignment to any less important variable. In this paper, we s...

The idea of ordering plays a basic role in commonsense reasoning for addressing three interrelated tasks: inconsistency handling, belief revision and plausible inference. We study the behavior of non-monotonic inferences induced by various methods for priority-based handling of inconsistent sets of classical formulas. One of them is based on a lexicographic ordering of maximal consistent subset...

KBlab is a Completion based theorem prover for equational logic, written in the language C and developed on the Macintosh in the MPW (Macintosh Programmer Workshop) programming environment. The core of KBlab is the Knuth–Bendix Completion Procedure (KB) [9,7,1], extended to Unfailing Knuth– Bendix (UKB) [5], S–strategy [5] and inductive theorem proving (IKB). IKB implements the Huet–Hullot meth...

We prove that the radix cross-section of a rational set for a length morphism, and more generally for a rational function from a free monoid into N, is rational, a property that does not hold any more if the image of the function is a subset of a free monoid with two or more generators. proceedings short version1 The purpose of this paper is to give a positive answer to a problem left open in a...

An algebraic linear ordering is a component of the initial solution of a first-order recursion scheme over the continuous categorical algebra of countable linear orderings equipped with the sum operation and the constant 1. Due to a general Mezei-Wright type result, algebraic linear orderings are exactly those isomorphic to the linear ordering of the leaves of an algebraic tree. Moreover, using...

In the framework of data imputation, this paper provides a non-parametric approach to missing data imputation based on Information Retrieval. In particular, an incremental procedure based on the iterative use of a tree-based method is proposed and a suitable Incremental Imputation Algorithm is introduced. The key idea is to define a lexicographic ordering of cases and variables so that conditio...

We give a new, and hopefully more easily understandable, structural proof of the decomposition of a k-valued transducer into k unambiguous functional ones, a result established by A. Weber in 1996. Our construction is based on a lexicographic ordering of computations of automata and on two coverings that can be build by means of this ordering. The complexity of the construction, measured as the...

Two kinds of orderings are widely used in term rewriting and theorem proving, namely recursive path ordering (RPO) and Knuth-Bendix ordering (KBO). They provide powerful tools to prove the termination of rewriting systems. They are also applied in ordered resolution to prune the search space without compromising refutational completeness. Solving ordering constraints is therefore essential to t...