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103
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 91 (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.
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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Secondorder logic and foundations of mathematics
 The Bulletin of Symbolic Logic
, 2001
"... We discuss the differences between firstorder set theory and secondorder logic as a foundation for mathematics. We analyse these languages in terms of two levels of formalization. The analysis shows that if secondorder logic is understood in its full semantics capable of characterizing categorical ..."
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Cited by 29 (3 self)
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We discuss the differences between firstorder set theory and secondorder logic as a foundation for mathematics. We analyse these languages in terms of two levels of formalization. The analysis shows that if secondorder logic is understood in its full semantics capable of characterizing categorically central mathematical concepts, it relies entirely on informal reasoning. On the other hand, if it is given a weak semantics, it loses its power in expressing concepts categorically. Firstorder set theory and secondorder logic are not radically different: the latter is a major fragment of the former. 1
Computational complexity of polyadic lifts of generalized quantifiers in natural language
, 2010
"... We study the computational complexity of polyadic quantifiers in natural language. This type of quantification is widely used in formal semantics to model the meaning of multiquantifier sentences. First, we show that the standard constructions that turn simple determiners into complex quantifiers, ..."
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Cited by 20 (11 self)
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We study the computational complexity of polyadic quantifiers in natural language. This type of quantification is widely used in formal semantics to model the meaning of multiquantifier sentences. First, we show that the standard constructions that turn simple determiners into complex quantifiers, namely Boolean operations, iteration, cumulation, and resumption, are tractable. Then, we provide an insight into branching operation yielding intractable natural language multiquantifier expressions. Next, we focus on a linguistic case study. We use computational complexity results to investigate semantic distinctions between quantified reciprocal sentences. We show a computational dichotomy between different readings of reciprocity. Finally, we go more into philosophical speculation on meaning, ambiguity and computational complexity. In particular, we investigate a possibility of revising the Strong Meaning Hypothesis with complexity aspects to better account for meaning shifts in the domain of multiquantifier sentences. The paper not only contributes to the field of formal semantics but also illustrates how the tools of computational complexity theory might be successfully used in linguistics and philosophy with an eye towards cognitive science.
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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Cited by 12 (1 self)
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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
What does it mean to say that logic is formal
, 2000
"... Much philosophy of logic is shaped, explicitly or implicitly, by the thought that logic is distinctively formal and abstracts from material content. The distinction between formal and material does not appear to coincide with the more familiar contrasts between a priori and empirical, necessary and ..."
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Cited by 10 (0 self)
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Much philosophy of logic is shaped, explicitly or implicitly, by the thought that logic is distinctively formal and abstracts from material content. The distinction between formal and material does not appear to coincide with the more familiar contrasts between a priori and empirical, necessary and contingent, analytic and synthetic—indeed, it is often invoked to explain these. Nor, it turns out, can it be explained by appeal to schematic inference patterns, syntactic rules, or grammar. What does it mean, then, to say that logic is distinctively formal? Three things: logic is said to be formal (or “topicneutral”) (1) in the sense that it provides constitutive norms for thought as such, (2) in the sense that it is indifferent to the particular identities of objects, and (3) in the sense that it abstracts entirely from the semantic content of thought. Though these three notions of formality are by no means equivalent, they are frequently run together. The reason, I argue, is that modern talk of the formality of logic has its source in Kant, and these three notions come together in the context of Kant’s transcendental philosophy. Outside of this context (e.g., in Frege), they can come apart. Attending to this
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.
A Compositional Game Semantics for MultiAgent Logics of Partial Information
"... 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