Informational Independence as a Semantical Phenomenon

Hintikka, Jaakko; Sandu, Gabriel

doi:10.1016/s0049-237x(08)70066-1

Cited by 113 publications

(106 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The next major development was the introduction of IF-logic ("independence-friendly logic") by Hintikka and Sandu (1989). The intention of IF-logic is to highlight informational dependence and independence.…”

Section: Further Developmentsmentioning

confidence: 99%

From IF to BI

Abramsky

Väänánen²

2008

Synthese

119

View full text Add to dashboard Cite

We take a fresh look at the logics of informational dependence and independence of Hintikka and Sandu and Väänänen, and their compositional semantics due to Hodges. We show how Hodges' semantics can be seen as a special case of a general construction, which provides a context for a useful completeness theorem with respect to a wider class of models. We shed some new light on each aspect of the logic. We show that the natural propositional logic carried by the semantics is the logic of Bunched Implications due to Pym and O'Hearn, which combines intuitionistic and multiplicative connectives. This introduces several new connectives not previously considered in logics of informational dependence, but which we show play a very natural rôle, most notably intuitionistic implication. As regards the quantifiers, we show that their interpretation in the Hodges semantics is forced, in that they are the image under the general construction of the usual Tarski semantics; this implies that they are adjoints to substitution, and hence uniquely determined. As for the dependence predicate, we show that this is definable from a simpler predicate, of constancy or dependence on nothing. This makes essential use of the intuitionistic implication. The Armstrong axioms for functional dependence are then recovered as a standard set of axioms for intuitionistic implication. We also prove a full abstraction result in the style of Hodges, in which the intuitionistic implication plays a very natural rôle.

show abstract

Section: Further Developmentsmentioning

confidence: 99%

From IF to BI

Abramsky

Väänánen²

2008

Synthese

119

View full text Add to dashboard Cite

show abstract

“…Independence-friendly logic (IF logic) is a conservative extension of first-order logic that has the same expressive power as existential second-order logic [6,7]. In IF logic the truth of a sentence is defined via a game between two players, Abélard (∀) and Eloïse (∃).…”

Section: Mathematics Subject Classification (2000)mentioning

confidence: 99%

Perfect IFG-Formulas

Mann

2008

Log. univers.

View full text Add to dashboard Cite

IFG logic is a variant of the independence-friendly logic of Hintikka and Sandu. We answer the question: "Which IFG-formulas are equivalent to ordinary first-order formulas?" We use the answer to prove the ordinary cylindric set algebra over a structure can be embedded into a reduct of the IFG-cylindric set algebra over the structure. Mathematics Subject Classification (2000). Primary 03G25; Secondary 03B60, 03G15.Independence-friendly logic (IF logic) is a conservative extension of first-order logic that has the same expressive power as existential second-order logic [6,7]. In IF logic the truth of a sentence is defined via a game between two players, Abélard (∀) and Eloïse (∃). The additional expressivity is obtained by modifying the quantifiers and connectives of an ordinary first-order sentence in order to restrict the information available to the existential player, Eloïse, in the associated semantic game.In IF logic, only the information available to Eloïse is restricted, which means existential quantifiers are not dual to universal quantifiers. To compensate, negation symbols are only allowed before atomic formulas. Generalized independencefriendly logic (IFG logic) is a variant of independence-friendly logic in which the information available to both players can be restricted, making existential quantifiers dual to universal quantifiers and allowing any formula to be negated [2]. Definition 1.1. Given a first-order signature σ, an atomic IFG-formula is a pair φ, X where φ is an atomic first-order formula and X is a finite set of variables that includes every variable that appears in φ (and possibly more).Definition 1.2. Given a first-order signature σ, the language L σ IFG is the smallest set of formulas such that:

show abstract

“…We start by introducing Partial Information logic (PI) which is a generalization of both first-order logic and Hintikka-Sandu [5] IF-logic. We motivate this logic by means of an example.…”

Section: Introductionmentioning

confidence: 99%