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...

This paper provides a new, decidable definition of the higherorder recursive path ordering in which type comparisons are made only when needed, therefore eliminating the need for the computability closure, and bound variables are handled explicitly, making it possible to handle recursors for arbitrary strictly positive inductive types.

In classical logics, the meaning of a formula is invariant with respect to the renaming of bound variables. This property, normally taken for granted, has been shown not to hold in the case of Independence Friendly (IF) logics. In this paper we argue that this is not an inherent characteristic of these logics but a defect in the way in which the compositional semantics given by Hodges for the r...

“prove((E,F),A,B,C,D) :!, prove(E,[F|A],B,C,D). prove((E;F),A,B,C,D) :!, prove(E,A,B,C,D), prove(F,A,B,C,D). prove(all(H,I),A,B,C,D) :!, \+length(C,D), copy_term((H,I,C),(G,F,C)), append(A,[all(H,I)],E), prove(F,E,B,[G|C],D). prove(A,_,[C|D],_,_) :((A= -(B); -(A)=B)) -> (unify(B,C); prove(A,[],D,_,_)). prove(A,[E|F],B,C,D) :prove(E,F,[A|B],C,D).” implements a first-order theorem prover based on...

We study a generalized version of the index calculus method for the discrete logarithm problem in Fq , when q = pn, p is a small prime and n→∞. The database consists of the logarithms of all irreducible polynomials of degree between given bounds; the original version of the algorithm uses lower bound equal to one. We show theoretically that the algorithm has the same asymptotic running time as ...

Let A be a well-formed formula of first-order modal logic whose only free variable is x. We shall use the following abbreviations: Mat(A) for (x)[OA * 0~A] Form(A) for (x)[DA vD-i] Ban(A) for ((x)DA) v ((x)U~A) Pred(A) for Form(A) v Mat(A). We read Mat(A), FormjA), and Ban(A) respectively as: "A is material", "A is formal", and "A is banal"; Pred(A) is the assertion of the Principle of Predica-...

A real-time process algebra, called ACSR, has been developed to facilitate the specification and analysis of real-time systems. ACSR supports synchronous timed actions and asynchronous instantaneous events. Timed actions are used to represent the usage of resources and to model the passage of time. Events are used to capture synchronization between processes. To be able to specify real-time sys...