The aim of Belief Merging is to aggregate possibly conflicting pieces of information issued from different sources. The quality of the resulting set is usually considered in terms of a closeness criterion between the resulting belief set and the initial belief sets. The notion of distance between belief sets is thus a crucial issue when we face the merging problem. The aim of this paper is twof...

We present the concept of a disjunctive basis as a generic framework for normal forms in modal logic based on coalgebra. Disjunctive bases were defined in previous work on completeness for modal fixpoint logics, where they played a central role in the proof of a generic completeness theorem for coalgebraic mu-calculi. Believing the concept has a much wider significance, here we investigate it m...

—In this paper, we examine and compare De Morgan-, Kleene-, and Boolean-disjunctive and conjunctive normal forms and consider their role in fuzzy settings. In particular, we show that there are normal forms and truth tables for classical fuzzy propositional logic and intervalvalued fuzzy propositional logic that are completely analogous to those for Boolean propositional logic. Thus, determinin...

The problem of local linearizability of the planar linear center nonlinearly perturbed is far from being solved even for low degree nonlinearity (n ≥ 3). Synchronization problem [1, 2] consists in bringing appropriate modifications on a given system to obtain a desired dynamic. The desired phase portrait along this contribution contains a compact region around a singular point at the origin in ...

We study the problem of defining normal forms of terms for the algebraic λ-calculus, an extension of the pure λ-calculus where linear combinations of terms are first-class entities: the set of terms is enriched with a structure of vector space, or module, over a fixed semiring. Towards a solution to the problem, we propose a variant of the original reduction notion of terms which avoids annoyin...

The paper gives a simple result on the existence of normal forms for the following equivalence relation between objects of a category: A B if and only if there are maps A ?! B and B ?! A, under the hypothesis that the category has epi-mono factorizations and each object has nitely many sub-objects and quotient-objects. Applications to algebra, logic, automata theory, databases are presented. Ge...

In Poincar e Normal Form theory, one considers a series of transformations generated by homogeneous polynomials obtained as solution of the homological equation; such solutions are unique up to terms in the kernel of the homological operator. By a careful exploitation of higher order eeects { which requires the solution of \higher order homological equations" { we show that the Poincar e normal...

A “partial” generalization of Fine’s definition [Fin] of normal forms in normal minimal modal logic is given. This means quick access to complete axiomatizations and decidability proofs for partial modal logic [Thi]. Introduction. From the viewpoint of formal linguistics, cognitive science and artificial intelligence, there appears to be a natural interest in the combinations of partiality and ...

In this paper we study induction of unrestricted clausal theories from interpretations. First, we show that in the propositional case induction from complete evidence can be seen as an equivalence-preserving transformation from DNF to CNF. From this we conclude that induction i s essentially a process of determining what is false in the domain of discourse. We then proceed by investigating dual...