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Finite Proofs for Infinitary Formulas
"... Abstract. Recent work has shown that the infinitary logic of hereandthere is closely related to the input language of the ASP grounder gringo. A formal system axiomatizing that logic exists, but a proof in that system may include infinitely many formulas. In this note, we define a correspondence b ..."
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Abstract. Recent work has shown that the infinitary logic of hereandthere is closely related to the input language of the ASP grounder gringo. A formal system axiomatizing that logic exists, but a proof in that system may include infinitely many formulas. In this note, we define a correspondence
A Model Existence Theorem for Infinitary Formulas in Metric Spaces
, 2008
"... We prove a Model Existence Theorem for a fully infinitary logic LA for metric structures. This result is based on a generalization of the notions of approximate formulas and approximate truth in normed structures introduced by Henson ([7]) and studied in different forms by Anderson ([1]) and Fajardo ..."
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We prove a Model Existence Theorem for a fully infinitary logic LA for metric structures. This result is based on a generalization of the notions of approximate formulas and approximate truth in normed structures introduced by Henson ([7]) and studied in different forms by Anderson ([1
INFINITARY LANGUAGES by
"... We begin with the following quotation from Karp [1964]: My interest in infinitary logic dates back to a February day in 1956 when I remarked to my thesis supervisor, Professor Leon Henkin, that a particularly vexing problem would be so simple if only I could write a formula which would say x = 0 or ..."
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We begin with the following quotation from Karp [1964]: My interest in infinitary logic dates back to a February day in 1956 when I remarked to my thesis supervisor, Professor Leon Henkin, that a particularly vexing problem would be so simple if only I could write a formula which would say x = 0
The semantics of Gringo and infinitary propositional formulas
 In Proceedings of International Conference on Principles of Knowledge Representation and Reasoning (KR
, 2014
"... Input languages of answer set solvers are based on the mathematically simple concept of a stable model. But many useful constructs available in these languages, including local variables, conditional literals, and aggregates, cannot be easily explained in terms of stable models in the sense of the ..."
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Cited by 2 (2 self)
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the problem of defining the semantics of GRINGO programs by translating them into the language of infinitary propositional formulas. This semantics allows us to study equivalent transformations of GRINGO programs using natural deduction in infinitary propositional logic, so that the properties
Infinitary Algebraic Specifications for Stream Algebras
"... Abstract. A stream is an infinite sequence of data from a set A. A wide variety of algorithms and architectures operate continuously in time, producing streams of data, for example: systolic arrays, dataflow machines, neural networks and cellular automata. Also many models of real number computatio ..."
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work with infinitary terms called stream terms, and infinitary formulae that generalise conditional equations, called ωconditional stream equations. 0
Computing with Infinitary Logic
 Theoretical Computer Science
, 1995
"... Most recursive extensions of relational calculus converge around two central classes of queries: fixpoint and while. Infinitary logic (with finitely many variables) is a very powerful extension of these languages which provides an elegant unifying formalism for a wide variety of query languages. ..."
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Cited by 10 (6 self)
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wellknown query languages are related to infinitary logic using syntactic restrictions formula...
Hierarchies in Transitive Closure Logic, Stratified Datalog and Infinitary Logic
 ANNALS OF PURE AND APPLIED LOGIC
, 1994
"... We establish a general hierarchy theorem for quantifier classes in the infinitary logic L ! 1! on finite structures. In particular, it is shown that no infinitary formula with bounded number of universal quantifiers can express the negation of a transitive closure. This implies the solution of se ..."
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Cited by 14 (4 self)
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We establish a general hierarchy theorem for quantifier classes in the infinitary logic L ! 1! on finite structures. In particular, it is shown that no infinitary formula with bounded number of universal quantifiers can express the negation of a transitive closure. This implies the solution
Infinitary Initial Algebra Specifications For Stream Algebras
 CONFORMATIONAL SELFASSEMBLY, PACI SYMPOSIUM ON BIOCOMPUTING'98
, 1998
"... A stream is an in nite sequence of data from a set A. A wide variety of algorithms and architectures operate continuously in time, processing streams of data, for example: hardware systems, embedded systems and emergent systems. Also many models of real number computation use streams. In this paper ..."
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Cited by 4 (4 self)
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called stream terms, and infinitary formulae that generalise conditional equations, called !conditional stream equations. We state a BirkhoffMal'cev type theorem that shows conservativity for the manysorted stream version of full infinitary firstorder logic L! 1 ! over an !conditional
Infinitary Logic and Inductive Definability over Finite Structures
 Information and Computation
, 1995
"... The extensions of firstorder logic with a least fixed point operator (FO + LFP) and with a partial fixed point operator (FO + PFP) are known to capture the complexity classes P and PSPACE respectively in the presence of an ordering relation over finite structures. Recently, Abiteboul and Vianu [Abi ..."
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Cited by 58 (7 self)
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as fragments of an infinitary logic where each formula has a bounded number of variables, L ! 1! (see, for instance, [Kolaitis and Vardi, 1990]). We investigate this logic of finite structures and provide a normal form for it. We also present a treatment of the results in [Abiteboul and Vianu, 1991b] from
Results 1  10
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