We present constructive arithmetic in Deduction modulo with rewrite rules only. In natural deduction and in sequent calculus, the cut elimination theorem and the analysis of the st...
We generalize the notion of slice introduced in our earlier paper [6]. A slice of a distributed computation with respect to a global predicate is the smallest computation that cont...
Let M = (A, <, P) where (A, <) is a linear ordering and P denotes a finite sequence of monadic predicates on A. We show that if A contains an interval of order type or -, an...
An NP search problem is the problems of finding a witness to the given NP predicate, and TFNP is the class of total NP search problems. TFNP contains a number of subclasses conta...
It is known that the first-order theory with a single predicate → that denotes one-step rewriting reduction on terms is undecidable already for formulae with ∃∀ prefix. Sev...