We present a new class of second-order uniication problems, which we have called linear. We deal with completely general second-order typed uniication problems, but we restrict the set of uniiers under consideration: they instantiate free variables by linear terms, i.e. terms where any-abstractions bind one and only one occurrence of a bound variable. Linear second-order uniication properly ext...

A recent development in the theory of M-sets has paved a new means of an approach to CH. Here we further clarify the theory and form part two of our previous paper[P]. The set B i will be used to represent binary numbers. A set of positions associated with a one symbol we will denote by pos Elements of pos we will denote by p(1) j. Sets of transformations T i. A knowable set H is denoted by K(H...

Existing machines for lazy evaluation use a flat representation of environments, storing the terms associated with free variables in an array. Combined with a heap, this structure supports the shared intermediate results required by lazy evaluation. We propose and describe an alternative approach that uses a shared environment to minimize the overhead of delayed computations. We show how a shar...

It is shown how by using results from combinatory logic an applicative language, such as LISP, can be translated into a form from which all bound variables have been removed. A machine is described which can efficiently execute the resulting code. This implementation is compared with a conventional interpreter and found to have a number of advantages. Of these the most important is that program...

In this paper we investigate the role played by one aspect of context, namely encyclopedic knowledge, to the interpretation of clause arguments. We discuss cases where the assignment of a specific semantic role of a predicate to a clause argument is not determined by the grammar alone, but requires extragrammatical resources (in particular, world knowledge), and then present a formally explicit...

We present an algorithm for counting the number of integer solutions to selected free variables of a Presburger formula. We represent the Presburger formula as a deterministic finite automaton (DFA) whose accepting paths encode the standard binary representations of satisfying free variable values. We count the number of accepting paths in such a DFA to obtain the number of solutions without en...

Tableau–Based theorem provers can be extended to cover many of the nonclassical logics currently used in AI research. For both, classical and nonclassical first–order logic, equality is a crucial feature to increase expressivity of the object language. Unfortunately, all so far existing attempts of adding equality to semantic tableaux have been more or less experimental and turn out to be usele...

This paper demonstrates that genetic programming can be used to create a circuit-constructing computer program that contains both conditional operations and inputs (free variables). The conditional operations and free variables enable a single genetically evolved program to yield functionally and topologically different electrical circuits. The conditional operations can trigger the execution o...

Second-order logic, it has been alleged by W. V. Quine [17], is nothing but set theory in disguise, and hence not logic proper. The second-order quantifiers, so the allegation goes, have to range over some kind of “higher” entity or universal: properties or attributes at worst; sets at best, as sets at least are extensional. Moreover, a set-theoretic understanding may allow us to appreciate tha...