We show how and why it makes sense to use a relational formalisation instead of the usual functional one in the treatment of term graphs. Special attention is paid to term graphs with bound variables, that have, to our knowledge, never been formalised with such a generality before. Besides the novel treatment of term graphs themselves, we present an innovative relational homomorphism concept th...

Ala~traet--Errors-in-variables problems are considered for the case of three variables, where the underlying relations among the noise-free variables are linear, and covariance information for the noisy variables is available. The static problem where the variables are complex (which can arise when narrowband filtering is used) is analysed in detail. Some results are also presented for the case...

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...