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Meaningless Sets in Infinitary Combinatory Logic
"... In this paper we study meaningless sets in infinitary combinatory logic. So far only a handful of meaningless sets were known. We show that there are uncountably many meaningless sets. As an application to the semantics of finite combinatory logics, we show that there exist uncountably many combinat ..."
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In this paper we study meaningless sets in infinitary combinatory logic. So far only a handful of meaningless sets were known. We show that there are uncountably many meaningless sets. As an application to the semantics of finite combinatory logics, we show that there exist uncountably many
Decomposing the Lattice of Meaningless Sets in the Infinitary Lambda Calculus
"... Abstract. The notion of a meaningless set has been defined for infinitary lambda calculus axiomatically. Standard examples of meaningless sets are sets of terms that have no head normal form, the set of terms without weak head normal form and the set of rootactive terms. The collection of meaningles ..."
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Abstract. The notion of a meaningless set has been defined for infinitary lambda calculus axiomatically. Standard examples of meaningless sets are sets of terms that have no head normal form, the set of terms without weak head normal form and the set of rootactive terms. The collection
Stationary sets and infinitary logic
 Journal of Symbolic Logic
, 2000
"... 657 revision:19970608 modified:19970608 Let K0 λ be the class of structures 〈λ, <, A〉, where A ⊆ λ is disjoint from a club, and let K 1 λ be the class of structures 〈λ, <, A〉, where A ⊆ λ contains a club. We prove that if λ = λ <κ is regular, then no sentence of Lλ + κ separates K0 λ an ..."
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Cited by 3 (2 self)
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657 revision:19970608 modified:19970608 Let K0 λ be the class of structures 〈λ, <, A〉, where A ⊆ λ is disjoint from a club, and let K 1 λ be the class of structures 〈λ, <, A〉, where A ⊆ λ contains a club. We prove that if λ = λ <κ is regular, then no sentence of Lλ + κ separates K0 λ and K1 λ. On the other hand, we prove that if λ = µ+, µ = µ<µ, and a forcing axiom holds (and ℵL 1 = ℵ1 if µ = ℵ0), then there is a sentence of Lλλ which separates K 0 λ and K1 λ. One of the fundamental properties of Lω1ω is that although every countable ordinal itself is definable in Lω1ω, the class of all countable wellordered structures is not. In particular, the classes K 0 = {〈ω, R 〉 : R wellorders ω} K 1 = {〈λ, R 〉 : 〈ω, R 〉 contains a copy of the rationals} cannot be separated by any Lω1ωsentence. In this paper we consider infinite quantifier languages Lκλ, λ> ω. Here wellfoundedness is readily definable, but we may instead consider the class Tλ = {〈λ, R 〉 : 〈λ, R 〉 is a tree with no branches of length λ}.
Complete Infinitary Type Logics
, 1997
"... For each regular cardinal , we set up three systems of infinitary type logic, in which the length of the types and the length of the typed syntactical constructs is ! . For a fixed , these three versions are (in the order of increasing strength): (1) the local system \Sigma () , (2) the global syste ..."
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For each regular cardinal , we set up three systems of infinitary type logic, in which the length of the types and the length of the typed syntactical constructs is ! . For a fixed , these three versions are (in the order of increasing strength): (1) the local system \Sigma () , (2) the global
NonDenumerable Infinitary Modal Logic
"... Abstract: Segerberg established an analogue of the canonical model theorem in modal logic for infinitary modal logic. However, the logics studied by Segerberg and Goldblatt are based on denumerable sets of pairs 〈Γ, α 〉 of sets Γ of wellformed formulae and wellformed formulae α. In this paper I sh ..."
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Abstract: Segerberg established an analogue of the canonical model theorem in modal logic for infinitary modal logic. However, the logics studied by Segerberg and Goldblatt are based on denumerable sets of pairs 〈Γ, α 〉 of sets Γ of wellformed formulae and wellformed formulae α. In this paper I
Logical preference representation and combinatorial vote,
 Annals of Mathematics and Artificial Intelligence
, 2004
"... We introduce the notion of combinatorial vote, where a group of agents (or voters) is supposed to express preferences and come to a common decision concerning a set of nonindependent variables to assign. We study two key issues pertaining to combinatorial vote, namely preference representation and ..."
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Cited by 96 (16 self)
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We introduce the notion of combinatorial vote, where a group of agents (or voters) is supposed to express preferences and come to a common decision concerning a set of nonindependent variables to assign. We study two key issues pertaining to combinatorial vote, namely preference representation
Coalgebraic Logic
 Annals of Pure and Applied Logic
, 1999
"... We present a generalization of modal logic to logical systems which are interpreted on coalgebras of functors on sets. The leading idea is that infinitary modal logic contains characterizing formulas. That is, every modelworld pair is characterized up to bisimulation by an infinitary formula. The ..."
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Cited by 110 (0 self)
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We present a generalization of modal logic to logical systems which are interpreted on coalgebras of functors on sets. The leading idea is that infinitary modal logic contains characterizing formulas. That is, every modelworld pair is characterized up to bisimulation by an infinitary formula
A note on extensions of infinitary logic
 Arch. Math. Logic
, 2005
"... 726 revision:20010608 modified:20010612 We show that a strong form of the so called Lindström’s Theorem [4] fails to generalize to extensions of Lκω and Lκκ: For weakly compact κ there is no strongest extension of Lκω with the (κ, κ)compactness property and the LöwenheimSkolem theorem down to κ ..."
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Cited by 2 (0 self)
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to κ. With an additional settheoretic assumption, there is no strongest extension of Lκκ with the (κ, κ)compactness property and the LöwenheimSkolem theorem down to < κ. By a wellknown theorem of Lindström [4], first order logic Lωω is the strongest logic which satisifies the compactness theorem
Predicate Logic Unplugged
 In Proceedings of the 10th Amsterdam Colloquium
, 1995
"... this paper we describe the syntax and semantics of a description language for underspecified semantic representations. This concept is discussed in general and in particular applied to Predicate Logic and Discourse Representation Theory. The reason for exploring underspecified representations as sui ..."
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Cited by 156 (7 self)
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this paper we describe the syntax and semantics of a description language for underspecified semantic representations. This concept is discussed in general and in particular applied to Predicate Logic and Discourse Representation Theory. The reason for exploring underspecified representations
Infinitary queries in spatial databases
, 2007
"... We describe the use of infinitary logics computable over the real numbers (i.e. in the sense of Blum–Shub–Smale, with fullprecision arithmetic) as a constraint query language for spatial databases. We give a characterization of the sets definable in various syntactic classes corresponding to the cl ..."
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Cited by 2 (2 self)
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We describe the use of infinitary logics computable over the real numbers (i.e. in the sense of Blum–Shub–Smale, with fullprecision arithmetic) as a constraint query language for spatial databases. We give a characterization of the sets definable in various syntactic classes corresponding
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