In computational function learning in the limit, an algorithmic learner tries to nd a program for a computable function g given successively more values of g, each time outputting a conjectured program for g. A learner is called postdictively complete i all available data is correctly postdicted by each conjecture. Akama and Zeugmann presented, for each choice of natural number δ, a relaxation ...

In this paper, among others, we prove the following results: (1) Let (X, d) be a complete cone metric space partially ordered by v and q be a c-distance on X. Suppose F : X × X → X and g : X → X be two continuous and commuting functions with F (X × X) ⊆ g(X). Let F satisfy mixed g-monotone property and q(F (x, y), F (u, v)) k2 (q(gx, gu) + q(gy, gv)) for some k ∈ [0, 1) and all x, y, u, v ∈ X w...

" Mathematicians care no more for logic than logicians for mathematics. " Augustus de Morgan, 1868 Proofs are traditionally syntactic, inductively generated objects. This paper presents an abstract mathematical formulation of propositional calculus (propositional logic) in which proofs are combinatorial (graph-theoretic), rather than syntactic. It defines a combinatorial proof of a proposition ...

A masure (also known as an affine ordered hovel) is a generalization of the Bruhat-Tits building that associated with split Kac-Moody group G over nonarchimedean local field. This union spaces called apartments. When reductive group, and there G-invariant distance inducing norm on each apartment. In this paper, we study distances topology We construct such element continuous automorphism their ...

(0, 1,2}. The set of three-valued logical functions (i.e., f: E” --t E for n=l,2,... ) is denoted by P3. A subset F of P3 is said to be closed if it contains all superpositions (i.e., compositions or substitutions) of its members (cf. [l, 1 l-131). For closed sets F and H such that FC H (proper inclusion), F is an H-maxima/ set if FC G c H for no closed set G. A subset F of H is complete in H i...

a generalization of schauder basis associated with the concept of generalized analytic functions is introduced. corresponding concepts of density, completeness, biorthogonality and basicity are defined. also, corresponding concept of the space of coefficients is introduced. under certain conditions for the  corresponding operators, some properties of the space of coefficients and basicity crite...