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...

Still the traditional design approach, and even more the Integrated Design Process, need an effective and efficient design methodology and smart, useful and fast design support tools, in order to fulfil the requirements of low energy buildings besides all other issues included in the “building design”: aesthetic, functionality, budget limit, customer requirements. How can the design team being ...

Prolog systems currently work with the restriction that negative subgoals not contain free variables, although some authors have suggested that this restriction can be lifted by running the theorem prover to exhaustion on the subgoal being considered. We suggest that this approach is likely not to be computationally viable in practice, and describe and formalize a new approach to dealing with q...

(1) ∀u, k∀v ≤ρ tuk∃w A0(u, k, v, w), where A0 is a quantifier–free formula 1 (containing only u, k, v, w as free variables) in the language of a suitable subsystem T ω of arithmetic in all finite types, t is a closed term and ≤ρ is defined pointwise (ρ being an arbitrary finite type). Lets suppose that (1) is provable in T . Then from a given such proof one can extract an effective uniform boun...

We consider the monodic formulas of common knowledge predicate logic, which allow applications of epistemic operators to formulas with at most one free variable. We provide nite axiomatizations of the monodic fragment of the most important common knowledge predicate logics (the full logics are known to be not recursively enumerable) and single out a number of their decidable fragments. On the o...

A formula '(x 1 ; : : :; x n) conforms to a partition P of fx 1 ; : : :; x n g if it is equivalent to a Boolean combination of formulae that do not have free variables from more than one block of P. We show that if ' conforms to two partitions P 1 and P 2 , it also conforms to their greatest lower bound in the partition lattice. As a corollary, we obtain that the concept of orthographic dimensi...