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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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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.
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.
Probabilistic Dependence Logic
, 2009
"... Given a finite model M, it is possible to associate to every sentence φ of Backslash Logic and Dependence Logic the value of the Nash equilibria of the corresponding imperfect information game H(φ). Hodges ’ compositional semantics can then be adapted to this new logic, and the value of atomic depen ..."
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Given a finite model M, it is possible to associate to every sentence φ of Backslash Logic and Dependence Logic the value of the Nash equilibria of the corresponding imperfect information game H(φ). Hodges ’ compositional semantics can then be adapted to this new logic, and the value of atomic dependence formulas in the resulting framework is seen to correspond to one of Kivinen and Mannila’s measures of approximate functional dependency.
On the Formal Semantics of IFlike Logics
"... Abstract. In classical logics, the meaning of a formula is invariant with respect to the renaming of bound variables. This property, normally taken for granted, has been shown not to hold in the case of Information Friendly (IF) logics. In this work we propose an alternative formalization under whic ..."
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Abstract. In classical logics, the meaning of a formula is invariant with respect to the renaming of bound variables. This property, normally taken for granted, has been shown not to hold in the case of Information Friendly (IF) logics. In this work we propose an alternative formalization under which invariance with respect the renaming of bound variables is restored. We show that, when one restricts to formulas where each variable is bound only once, our semantics coincide with those previously used in the literature. We also prove basic metatheoretical results of the resulting logic, such as compositionality and truth preserving operations on valuations. We work on Hodges ’ slash logic (from which results can be easily transferred to other IFlike logics) and we also consider his flattening operator, for which we give a gametheoretical semantics. 1
Declarations of Dependence
"... “Science is the knowledge of consequences, and dependence of one fact upon another.” Thomas Hobbes Dependence is one of these subtle concepts with so many connotations and usages, that any analysis of its meaning is predestined to fall short of some of its aspects. In the first paragraph of the book ..."
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“Science is the knowledge of consequences, and dependence of one fact upon another.” Thomas Hobbes Dependence is one of these subtle concepts with so many connotations and usages, that any analysis of its meaning is predestined to fall short of some of its aspects. In the first paragraph of the book Dependence Logic [9], Väänänen states: ‘Dependence is a common phenomenon, wherever one looks: ecological systems, astronomy, human history, stock markets. With global warming, the dependence of life on earth on the actions of mankind has become a burning issue. But what is the logic of dependence?’ The book promises a systematic study of the concept, and to show that there is a mathematical theory of dependence. The paper in this volume [10] goes even further. It presents a logic of ‘possible dependence’, where the intended sense of ‘dependence ’ is specified
On the Formal Semantics of IFlike Logics
, 2009
"... In classical logics, the meaning of a formula is invariant with respect to the renaming of bound variables. This property, normally taken for granted, has been shown not to hold in the case of Information Friendly (IF) logics. In this paper we argue that this is not an inherent characteristic of the ..."
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In classical logics, the meaning of a formula is invariant with respect to the renaming of bound variables. This property, normally taken for granted, has been shown not to hold in the case of Information Friendly (IF) logics. In this paper we argue that this is not an inherent characteristic of these logics but a defect in the way in which the compositional semantics given by Hodges for the regular fragment was generalized to arbitrary formulas. We fix this by proposing an alternative formalization, based on a variation of the classical notion of valuation. Basic metatheoretical results are proven. We present these results for Hodges' slash logic (from which these can be easily transferred to other IFlike logics) and we also consider the flattening operator, for which we give novel gametheoretical semantics.