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Inclusion and exclusion dependencies in team semantics: On some logics of imperfect information
 Annals of Pure and Applied Logic, 163(1):68
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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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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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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
Dependence and Independence ∗
, 2010
"... We introduce an atomic formula ⃗y ⊥⃗x ⃗z intuitively saying that the variables ⃗y are independent from the variables ⃗z if the variables ⃗x are kept constant. We contrast this with dependence logic D [5] based on the atomic formula =(⃗x, ⃗y), actually a special case of ⃗y ⊥⃗x ⃗z, saying that the var ..."
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We introduce an atomic formula ⃗y ⊥⃗x ⃗z intuitively saying that the variables ⃗y are independent from the variables ⃗z if the variables ⃗x are kept constant. We contrast this with dependence logic D [5] based on the atomic formula =(⃗x, ⃗y), actually a special case of ⃗y ⊥⃗x ⃗z, saying that the variables ⃗y are totally determined by the variables ⃗x. We show that ⃗y ⊥⃗x ⃗z gives rise to a natural logic capable of formalizing basic intuitions about independence and dependence. We show that ⃗y ⊥⃗x ⃗z can be used to give partially ordered quantifiers and IFlogic a compositional interpretation without some of the shortcomings related to so called signaling that interpretations using =(⃗x, ⃗y) have. Of the numerous uses of the word “dependence ” we focus on the concept of an attribute 1 depending on a number of other similar attributes when we observe the world. We call these attributes variables. We follow the approach of [5] and focus on the strongest form of dependence, namely functional dependence. This is the kind of dependence in which some given variables absolutely deterministically determine some
Inclusion Logic and Fixed Point Logic
"... We investigate the properties of Inclusion Logic, that is, First Order Logic with Team Semantics extended with inclusion dependencies. We prove that Inclusion Logic is equivalent to Greatest Fixed Point Logic, and we prove that all unionclosed firstorder definable properties of relations are defin ..."
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We investigate the properties of Inclusion Logic, that is, First Order Logic with Team Semantics extended with inclusion dependencies. We prove that Inclusion Logic is equivalent to Greatest Fixed Point Logic, and we prove that all unionclosed firstorder definable properties of relations are definable in it. We also provide an EhrenfeuchtFraïssé game for Inclusion Logic, and give an example illustrating its use.
Independent Choices and the Interpretation of IF Logic
 Journal of Logic, Language and Information
, 2002
"... Abstract. In this paper it is argued that Hintikka’s game theoretical semantics for Independence Friendly logic does not formalize the intuitions about independent choices; it rather is a formalization of imperfect information. Furthermore it is shown that the logic has several strange properties (e ..."
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Abstract. In this paper it is argued that Hintikka’s game theoretical semantics for Independence Friendly logic does not formalize the intuitions about independent choices; it rather is a formalization of imperfect information. Furthermore it is shown that the logic has several strange properties (e.g. renaming of bound variables is not allowed). An alternative semantics is proposed which formalizes intuitions about independence.
From formulas to cirquents in computability logic
, 2009
"... Computability logic (CL) is a recently introduced semantical platform and ambitious program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which logic has more traditionally been. Its expressions represent interactive computational tasks seen as ..."
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Computability logic (CL) is a recently introduced semantical platform and ambitious program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which logic has more traditionally been. Its expressions represent interactive computational tasks seen as games played by a machine against the environment, and “truth ” is understood as existence of an algorithmic winning strategy. With logical operators standing for operations on games, the formalism of CL is openended, and has already undergone series of extensions. This article extends the expressive power of CL in a qualitatively new way, generalizing formulas (to which the earlier languages of CL were limited) to circuitstyle structures termed cirquents. The latter, unlike formulas, are able to account for subgame/subtask sharing between different parts of the overall game/task. Among the many advantages offered by this ability is that it allows us to capture, refine and generalize the well known independencefriendly logic which, after the present leap forward, naturally becomes a conservative fragment of CL, just as classical logic had been known to be a conservative fragment of the formulabased version of CL. Technically, this paper is selfcontained, and can be read without any prior familiarity with CL.
Socially Responsive, Environmentally Friendly Logic
 in Truth and Games: Essays in Honour of Gabriel Sandu, Aho, Tuomo and AhtiVeikko Pietarinen, eds., Acta Philosophica Fennica
, 2006
"... We consider the following questions: What kind of logic has a natural semantics in multiplayer (rather than 2player) games? How can we express branching quantifiers, and other partialinformation constructs, with a properly compositional syntax and semantics? We develop a logic in answer to these ..."
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We consider the following questions: What kind of logic has a natural semantics in multiplayer (rather than 2player) games? How can we express branching quantifiers, and other partialinformation constructs, with a properly compositional syntax and semantics? We develop a logic in answer to these questions, with a formal semantics based on multiple concurrent strategies, formalized as closure operators on KahnPlotkin concrete domains. Partial information constraints are represented as coclosure operators. We address the syntactic issues by treating syntactic constituents, including quantifiers, as arrows in a category, with arities and coarities. This enables a fully compositional account of a wide