Connecting Logical Representations and Efficient Computations

A duality between LM-fuzzy possibility computations and their logical semantics

Let X be a dcpo and let L be a complete lattice. The family σL(X) of all Scott continuous mappings from X to L is a complete lattice under pointwise order, we call it the L-fuzzy Scott structure on X. Let E be a dcpo. A mapping g : σL(E) −> M is called an LM-fuzzy possibility valuation of E if it preserves arbitrary unions. Denote by πLM(E) the set of all LM-fuzzy possibility valuations of E. T...

Logical Speciications of Innnite Computations ?

Starting from an identiication of innnite computations with !-words, we present a framework in which diierent classiication schemes for speciica-tions are naturally compared. Thereby we connect logical formalisms with hierarchies of descriptive set theory (e.g., the Borel hierarchy), of recursion theory, and with the hierarchy of acceptance conditions of !-automata. In particular, it is shown i...

Admissible representations for continuous computations

A Logical Framework for Convergent Infinite Computations

Classical computations can not capture the essence of infinite computations very well. This paper will focus on a class of infinite computations called convergent infinite computations. A logic for convergent infinite computations is proposed by extending first order theories using Cauchy sequences, which has stronger expressive power than the first order logic. A class of fixed points characte...

Logical Foundations of Syllable Representations

• Differences in notation do not necessarily entail differences in the information encoded in a particular formalism. • Fonts are notationally equivalent, in the sense that cat and cat are the same word. • In contrast, there are meaningful differences between bracket types in mathematical notation: {1, 2} is an unordered set, while (1, 2) is an ordered pair. Research question: are different syl...