Abstract. Recent work has shown that the infinitary logic of here-and-there 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

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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

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 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 trans-formations of GRINGO programs using natural deduction in infinitary propositional logic, so that the properties

work with infinitary terms called stream terms, and infinitary formulae that generalise conditional equations, called ω-conditional stream equations. 0

well-known query languages are related to infinitary logic using syntactic restrictions formula...

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

called stream terms, and infinitary formulae that generalise conditional equations, called !-conditional stream equations. We state a Birkhoff-Mal'cev type theorem that shows conservativity for the many-sorted stream version of full infinitary first-order logic L! 1 ! over an !-conditional

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