the aim of this paper is to introduce the concepts of fuzzy upper and fuzzy lower almost continuous, weakly continuous and almost weakly continuous multifunctions. several characterizations and properties of these multifunctions along with their mutual relationships are established in $l$-fuzzy topological spaces

The paper consists of two parts. The rst one is a concise introduction to epistemic (both propositional and predicate) logic with common knowl-ege operator. As the full common knowledge predicate logics are not even recursively enumerable, in the second part we introduce and investigate the monodic fragment of these logics which allows applications of the epistemic operators to formulas with at...

Let z = (z1, z2, · · · , zn) be noncommutative free variables and t a formal parameter which commutes with z. Let k be a unital commutative ring of any characteristic and Ft(z) = z−Ht(z) with Ht(z) ∈ k[[t]]〈〈z〉〉 ×n and o(Ht(z)) ≥ 2. Note that Ft(z) can be viewed as a deformation of the formal map F (z) := z−Ht=1(z) when it makes sense. The inverse map Gt(z) of Ft(z) can always be written as Gt(...

In this paper we prove decidability of two kinds of branching time temporal logics. First we show that the non-local version of propositional , in which truth values of atoms may depend on the branch of evaluation, is decidable. Then we use this result to establish decidability of various fragments of quantified , where the next-time operator can be applied only to formulas with at most one fre...

Affine λ-terms are λ-terms in which each bound variable occurs at most once and linear λ-terms are λ-terms in which each bound variable occurs once. and only once. In this paper we count the number of closed affine λ-terms of size n, closed linear λ-terms of size n, affine β-normal forms of size n and linear β-normal forms of size n, for different ways of measuring the size of λ-terms. From the...

We consider reductions in Orthogonal Expression Reduction Systems (OERS), that is, Orthogonal Term Rewriting Systems with bound variables and substitutions, as in the-calculus. We design a strategy that for any given term t constructs a longest reduction starting from t if t is strongly normalizable, and constructs an innnite reduction otherwise. The Conservation Theorem for OERSs follows easil...

The paper considers the set ML1 of rst-order polymodal formulas the modal operators in which can be applied to subformulas of at most one free variable. Using the mosaic technique, we prove a general satissability criterion for formulas in ML1 which reduces the modal satissability to the classical one. The criterion is then used to single out a number of new, in a sense optimal, decidable fragm...

Environments and closures are two of the main ingredients of evaluation in lambdacalculus. A closure is a pair consisting of a lambda-term and an environment, whereas an environment is a list of lambda-terms assigned to free variables. In this paper we investigate some dynamic aspects of evaluation in lambda-calculus considering the quantitative, combinatorial properties of environments and clo...