Results 1  10
of
158,759
An Analysis of FirstOrder Logics of Probability
 Artificial Intelligence
, 1990
"... : We consider two approaches to giving semantics to firstorder logics of probability. The first approach puts a probability on the domain, and is appropriate for giving semantics to formulas involving statistical information such as "The probability that a randomly chosen bird flies is greater ..."
Abstract

Cited by 316 (18 self)
 Add to MetaCart
: We consider two approaches to giving semantics to firstorder logics of probability. The first approach puts a probability on the domain, and is appropriate for giving semantics to formulas involving statistical information such as "The probability that a randomly chosen bird flies
The Semantics of Predicate Logic as a Programming Language
 Journal of the ACM
, 1976
"... ABSTRACT Sentences in firstorder predicate logic can be usefully interpreted as programs In this paper the operational and fixpomt semantics of predicate logic programs are defined, and the connections with the proof theory and model theory of logic are investigated It is concluded that operational ..."
Abstract

Cited by 810 (18 self)
 Add to MetaCart
ABSTRACT Sentences in firstorder predicate logic can be usefully interpreted as programs In this paper the operational and fixpomt semantics of predicate logic programs are defined, and the connections with the proof theory and model theory of logic are investigated It is concluded
TwoVariable Logic with Counting is Decidable
, 1996
"... We prove that the satisfiability problem for C² is decidable. C² is firstorder logic with only two variables in the presence of arbitrary counting quantifiers 9 ?m , m ? 1. It considerably extends L², plain firstorder with only two variables, which is known to be decidable by a result of Mort ..."
Abstract

Cited by 76 (4 self)
 Add to MetaCart
We prove that the satisfiability problem for C² is decidable. C² is firstorder logic with only two variables in the presence of arbitrary counting quantifiers 9 ?m , m ? 1. It considerably extends L², plain firstorder with only two variables, which is known to be decidable by a result
Complexity Results for FirstOrder TwoVariable Logic with Counting
, 2000
"... Let C 2 p denote the class of first order sentences with two variables and with additional quantifiers "there exists exactly (at most, at least) i", for i p, and let C 2 be the union of C 2 p taken over all integers p. We prove that the satisfiability problem for C 2 1 sentences is NEXPTIM ..."
Abstract

Cited by 32 (1 self)
 Add to MetaCart
is NEXPTIMEcomplete. This strengthens the results by E. Grädel, Ph. Kolaitis and M. Vardi [15] who showed that the satisfiability problem for the first order twovariable logic L 2 is NEXPTIMEcomplete and by E. Grädel, M. Otto and E. Rosen [16] who proved the decidability of C 2 . Our result easily implies
Twovariable logic on data words
, 2007
"... In a data word each position carries a label from a finite alphabet and a data value from some infinite domain. These models have been already considered in the realm of semistructured data, timed automata and extended temporal logics. It is shown that satisfiability for the twovariable firstorder ..."
Abstract

Cited by 36 (4 self)
 Add to MetaCart
In a data word each position carries a label from a finite alphabet and a data value from some infinite domain. These models have been already considered in the realm of semistructured data, timed automata and extended temporal logics. It is shown that satisfiability for the twovariable firstorder
Undecidability Results on TwoVariable Logics
 IN PROCEEDINGS OF 14TH SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE STACS`97, LECTURE NOTES IN COMPUTER SCIENCE NR. 1200
, 1998
"... It is a classical result of Mortimer that L², firstorder logic with two variables, is decidable for satisfiability. We show that going beyond L² by adding any one of the following leads to an undecidable logic: ffl very weak forms of recursion, viz. (i) transitive closure operations (ii) (restrict ..."
Abstract

Cited by 33 (5 self)
 Add to MetaCart
It is a classical result of Mortimer that L², firstorder logic with two variables, is decidable for satisfiability. We show that going beyond L² by adding any one of the following leads to an undecidable logic: ffl very weak forms of recursion, viz. (i) transitive closure operations (ii
Temporal and modal logic
 HANDBOOK OF THEORETICAL COMPUTER SCIENCE
, 1995
"... We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic. ..."
Abstract

Cited by 1300 (17 self)
 Add to MetaCart
We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic.
A Framework for Defining Logics
 JOURNAL OF THE ASSOCIATION FOR COMPUTING MACHINERY
, 1993
"... The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed calculus with dependent types. Syntax is treated in a style similar to, but more general than, MartinLof's system of ariti ..."
Abstract

Cited by 807 (45 self)
 Add to MetaCart
of arities. The treatment of rules and proofs focuses on his notion of a judgement. Logics are represented in LF via a new principle, the judgements as types principle, whereby each judgement is identified with the type of its proofs. This allows for a smooth treatment of discharge and variable occurrence
Results 1  10
of
158,759