Results 1  10
of
1,609
Inductive Definitions with Decidable Atomic Formulas
"... . We introduce a type theory for infinitely branching trees, called the theory of free algebras. In this type theory we define an extensional equality based on decidable atomic formulas only. We show, that equality axioms, which add full extensionality to the theory, yield a conservative extension o ..."
Abstract
 Add to MetaCart
. We introduce a type theory for infinitely branching trees, called the theory of free algebras. In this type theory we define an extensional equality based on decidable atomic formulas only. We show, that equality axioms, which add full extensionality to the theory, yield a conservative extension
On Existentially Quantified Conjunctions of Atomic Formulae of ...
, 1997
"... Sufficient conditions for an 9 , 89 , or 889 prenex L + sentence to be translatable into the variablefree formalism L \Theta will be singled out in what follows. An efficient test based on such conditions will also be described. Through minor modifications of this testing algorithm, o ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
Sufficient conditions for an 9 , 89 , or 889 prenex L + sentence to be translatable into the variablefree formalism L \Theta will be singled out in what follows. An efficient test based on such conditions will also be described. Through minor modifications of this testing algorithm, one can obtain the translation when the sufficient conditions are met. 1 Introduction L \Theta is a ground equational formalism that can compete with firstorder predicate logic as a support for number theories as well as for fullblown theories of sets (cf. [TG87]). Superficially, it resembles the relational languages grown inside the database and knowledge base field more than the specification languages inspired by traditional logic. In analogy with firstorder logic, fragments of which have been endowed with an executable semantics, L \Theta has been proposed as a support for programming languages (cf. [BL92] and [FL94]). From the standpoint of automated deduction, L \Theta has the...
Dependence of variables construed as an atomic formula
 ANNALS OF PURE AND APPLIED LOGIC
, 2010
"... ..."
Arbitrary Alphabet. Syntax of Terms, Atomic Formulas and their Subterms1
"... Summary. Second of a series of articles laying down the bases for classical first order model theory. A language is defined basically as a tuple made of an integervalued function (adicity), a symbol of equality and a symbol for the NOR logical connective. The only requests for this tuple to be a la ..."
Abstract
 Add to MetaCart
], and the set of atomic formulas is introduced. The set of all terms is shown to be unambiguous with respect to concatenation; we say that it is a prefix set. This fact is exploited to uniquely define the subterms both of a term and of an atomic formula without resorting to a parse tree.
HiLog: A foundation for higherorder logic programming
 JOURNAL OF LOGIC PROGRAMMING
, 1993
"... We describe a novel logic, called HiLog, and show that it provides a more suitable basis for logic programming than does traditional predicate logic. HiLog has a higherorder syntax and allows arbitrary terms to appear in places where predicates, functions and atomic formulas occur in predicate calc ..."
Abstract

Cited by 252 (42 self)
 Add to MetaCart
We describe a novel logic, called HiLog, and show that it provides a more suitable basis for logic programming than does traditional predicate logic. HiLog has a higherorder syntax and allows arbitrary terms to appear in places where predicates, functions and atomic formulas occur in predicate
Right Type Departmental Bulletin Paper
"... Formulas with only one atomic formula in Grzegorczyk logic and provability logic * ..."
Abstract
 Add to MetaCart
Formulas with only one atomic formula in Grzegorczyk logic and provability logic *
Simplification of Quantifierfree Formulas over Ordered Fields
 Journal of Symbolic Computation
, 1995
"... this article is to provide a collection of practicable methods that have been implemented and extensively tested for their relevance. We further show how to combine different ideas for simplification in such a way that a formula is obtained which cannot be further simplified with any of the describe ..."
Abstract

Cited by 35 (16 self)
 Add to MetaCart
interactions between atomic formulas on different Boolean levels, it has turned out that this concept captures also other simplifiers that we had developed some time ago. These simplifiers, namely the Grobner simplifier and the Tableau simplifiers, could even be generalized due to this new viewpoint. 1
Lazy Satisfiability Modulo Theories
 JOURNAL ON SATISFIABILITY, BOOLEAN MODELING AND COMPUTATION 3 (2007) 141Â224
, 2007
"... Satisfiability Modulo Theories (SMT) is the problem of deciding the satisfiability of a firstorder formula with respect to some decidable firstorder theory T (SMT (T)). These problems are typically not handled adequately by standard automated theorem provers. SMT is being recognized as increasingl ..."
Abstract

Cited by 189 (50 self)
 Add to MetaCart
require testing the satisfiability of formulas which are Boolean combinations of atomic propositions and atomic expressions in T, so that heavy Boolean reasoning must be efficiently combined with expressive theoryspecific reasoning. The dominating approach to SMT (T), called lazy approach, is based
Loop Formulas for Logic Programs with Arbitrary Constraint Atoms
"... We formulate loop formulas for logic programs with arbitrary constraint atoms, for the semantics based on conditional satisfaction. This provides a method for answer set computation by computing models of completion. One particular attractive candidate for the latter task is pseudoboolean constrain ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
We formulate loop formulas for logic programs with arbitrary constraint atoms, for the semantics based on conditional satisfaction. This provides a method for answer set computation by computing models of completion. One particular attractive candidate for the latter task is pseudo
On Monotone Formula Closure of SZK
, 1994
"... We investigate structural properties of statistical zero knowledge (SZK) both in the interactive and in the noninteractive model. Specifically, we look into the closure properties of SZK languages under monotone logical formula composition. This gives rise to new protocol techniques. We show that i ..."
Abstract

Cited by 43 (2 self)
 Add to MetaCart
that interactive SZK for random self reducible languages (RSR) (and for coRSR) is closed under monotone boolean operations. Namely, we give SZK proofs for monotone boolean formulae whose atoms are statements about an SZK language which is RSR (or a complement of RSR). All previously known languages in SZK
Results 1  10
of
1,609