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Compositional Semantics for a Language of Imperfect Information
 LOGIC JOURNAL OF THE IPGL
, 1997
"... We describe a logic which is the same as firstorder logic except that it allows control over the information that passes down from formulas to subformulas. For example the logic is adequate to express branching quantifiers. We describe a compositional semantics for this logic; in particular this gi ..."
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Cited by 89 (2 self)
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We describe a logic which is the same as firstorder logic except that it allows control over the information that passes down from formulas to subformulas. For example the logic is adequate to express branching quantifiers. We describe a compositional semantics for this logic; in particular this gives a compositional meaning to formulas of the `informationfriendly' language of Hintikka and Sandu. For firstorder formulas the semantics reduces to Tarski's semantics for firstorder logic. We prove that two formulas have the same interpretation in all structures if and only if replacing an occurrence of one by an occurrence of the other in a sentence never alters the truthvalue of the sentence in any structure.
Independence: Logics and Concurrency
 P.O. Box 1047, Arlington, TX
, 2000
"... We consider Hintikka et al.'s `independencefriendly firstorder logic'. We apply it to a modal logic setting, defining a notion of `independent' modal logic, and we examine the associated fixpoint logics. ..."
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Cited by 13 (2 self)
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We consider Hintikka et al.'s `independencefriendly firstorder logic'. We apply it to a modal logic setting, defining a notion of `independent' modal logic, and we examine the associated fixpoint logics.
Logics of imperfect information: why sets of assignments
 Proceedings of 7th De Morgan Workshop ’Interactive Logic: Games and Social Software
, 2005
"... In 1961 Leon Henkin [3] extended firstorder logic by adding partially ordered arrays of quantifiers. He proposed a semantics for sentences φ that begin with quantifier arrays of this kind: φ is true in a structure A if and only if there are a sentence φ + and a structure A + such that: • φ + comes ..."
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Cited by 11 (0 self)
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In 1961 Leon Henkin [3] extended firstorder logic by adding partially ordered arrays of quantifiers. He proposed a semantics for sentences φ that begin with quantifier arrays of this kind: φ is true in a structure A if and only if there are a sentence φ + and a structure A + such that: • φ + comes from φ by removing each existential quantifier ∃y in the partially ordered prefix, and replacing each occurrence of the variable y by a term F (¯x) where ¯x are the variables universally quantified ‘before’ ∃y in the quantifier prefix (so that the new function symbols F are Skolem function symbols), • A + comes from A by adding functions to interpret the Skolem function symbols in φ +, and • φ + is true in A +. For example the sentence
ModelChecking Games for Logics of Imperfect Information
, 2012
"... Logics of dependence and independence have semantics that, unlike Tarski semantics, are not based on single assignments (mapping variables to elements of a structure) but on sets of assignments. Sets of assignments are called teams and the semantics is called team semantics. We design modelchecking ..."
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Logics of dependence and independence have semantics that, unlike Tarski semantics, are not based on single assignments (mapping variables to elements of a structure) but on sets of assignments. Sets of assignments are called teams and the semantics is called team semantics. We design modelchecking games for logics with team semantics in a general and systematic way. The construction works for any extension of firstorder logic by atomic formulae on teams, as long as certain natural conditions are observed which are satisified by all team properties considered so far in the literature, including dependence, independence, constancy, inclusion, and exclusion. The secondorder features of team semantics are reflected by the notion of a consistent winning strategy which is also a secondorder notion in the sense that it depends not on single plays but on the space of all plays that are compatible with the strategy. Beyond the application to logics with team semantics, we isolate an abstract, purely combinatorial definition of such games, which may be viewed as secondorder reachability games, and study their algorithmic properties. A number of examples are provided that show how logics with team semantics express familiar combinatorial problems in a somewhat unexpected way. Based on our games, we provide a complexity analysis of logics with teams semantics.
Complexity of twovariable Dependence Logic and IFLogic
, 2013
"... We study the twovariable fragments D2 and IF2 of dependence logic and independencefriendly logic. We consider the satisfiability and finite satisfiability problems of these logics and show that for D2, both problems are NEXPTIMEcomplete, whereas for IF2, the problems are Π 01 and Σ 0 1complete, ..."
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Cited by 6 (4 self)
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We study the twovariable fragments D2 and IF2 of dependence logic and independencefriendly logic. We consider the satisfiability and finite satisfiability problems of these logics and show that for D2, both problems are NEXPTIMEcomplete, whereas for IF2, the problems are Π 01 and Σ 0 1complete, respectively. We also show that D2 is strictly less expressive than IF2 and that already in D2, equicardinality of two unary predicates and infinity can be expressed (the latter in the presence of a constant symbol). This is an extended version of a publication in the proceedings of the 26th Annual
Computational interpretations of classical linear logic
 LNCS
, 2007
"... Abstract. We survey several computational interpretations of classical linear logic based on twoplayer onemove games. The moves of the games are higherorder functionals in the language of finite types. All interpretations discussed treat the exponentialfree fragment of linear logic in a common w ..."
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Abstract. We survey several computational interpretations of classical linear logic based on twoplayer onemove games. The moves of the games are higherorder functionals in the language of finite types. All interpretations discussed treat the exponentialfree fragment of linear logic in a common way. They only differ in how much advantage one of the players has in the exponentials games. We discuss how the several choices for the interpretation of the modalities correspond to various wellknown functional interpretations of intuitionistic logic, including Gödel’s Dialectica interpretation and Kreisel’s modified realizability. 1
Team building in dependence
"... Hintikka and Sandu’s IndependenceFriendly Logic was introduced as a logic for partially ordered quantification, in which the independence of (existential) quantifiers from previous (universal) quantifiers is written by explicit syntax. It was originally given a semantics by games of imperfect infor ..."
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Hintikka and Sandu’s IndependenceFriendly Logic was introduced as a logic for partially ordered quantification, in which the independence of (existential) quantifiers from previous (universal) quantifiers is written by explicit syntax. It was originally given a semantics by games of imperfect information; Hodges then gave a (necessarily) secondorder Tarskian semantics. More recently, Väänänen (2007) has proposed that the many curious features of IF logic can be better understood in his Dependence Logic, in which the (in)dependence of variables is stated in atomic formula, rather than by changing the definition of quantifier; he gives semantics in Tarskian form, via imperfect information games, and via a routine secondorder perfect information game. He then defines Team Logic, where classical negation is added to the mix, resulting in a full secondorder expressive logic. He remarks that no game semantics appears possible (other than by playing at second order). In this article, we explore an alternative approach to game semantics for DL, where we avoid imperfect information, yet stay locally apparently firstorder, by sweeping the secondorder information into longer games (infinite games in the case of countable models). Extending the game to Team Logic is not possible in standard games, but we conjecture a move to transfinite games may achieve a ‘natural ’ game for Team Logic.