Finite information logic

Parikh, Rohit; Väänánen, Jouko

doi:10.1016/j.apal.2004.06.013

Cited by 8 publications

(9 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Even more delicate flows of information were studied in the Partial Information logic by Parikh and Väänänen [32] whose formulae give rise to imperfect information games in which Eloise may be partially informed about the previous actions. In semantic games for the first-order formula ∀x∃y R(x, y), for instance, Eloise knows the object assigned to x.…”

Section: Propositionmentioning

confidence: 99%

1. Setting the Stage

2019

Ginseng and Aspirin

View full text Add to dashboard Cite

In this paper, we study the game-theoretic and computational repercussions of Henkin's partially ordered quantifiers [19]. After defining a gametheoretic semantics for these objects, we observe that tuning the parameter of absentmindedness gives rise to quantifier prefixes studied in [28]. In the interest of computation, we characterize the complexity class P NP in terms of partially ordered quantifiers, by means of a proof different from Gottlob's * We gratefully acknowledge Johan van Benthem, Peter van Emde Boas, Yuri Gurevich, Marcin Mostowski, Eric Pacuit, Gabriel Sandu, Tero Tulenheimo, and the anonymous reviewer. This paper was finalized at Stanford University, whom we thank for hosting us as a visiting scholar.

show abstract

Section: Propositionmentioning

confidence: 99%

1. Setting the Stage

2019

Ginseng and Aspirin

View full text Add to dashboard Cite

show abstract

“…One of the first results about database dependencies is the so called Armstrong Completeness Theorem [3]. It has as its starting point a set of axioms for the dependance =(x, y).…”

Section: Definition 1 a Team Is Any Set Of Assignments For A Fixed Smentioning

confidence: 99%

“…

…”

mentioning

confidence: 99%

The Logic of Approximate Dependence

Väänánen

2017

Outstanding Contributions to Logic

Self Cite

View full text Add to dashboard Cite

In my joint paper [3] with Rohit Parikh we investigate a logic arising from finite information. Here we consider another kind of limited information, namely information with a small number of errors, and prove a related completeness theorem. We point out that this approach naturally leads to considering multi-teams in the team semantics that lies behind [3].The idea of finite information logic [1] is that when quantifiers, especialy the existential quantifiers, express choices in social context, the choices are based on finite information about the parameters present. In this paper we consider a different kind of restriction. We do not restrict the information available but we allow a small number of errors. In social sofware a few errors can perhaps be allowed, especially if there is an agreement about it.

show abstract

“…Parikh's mathematical facility-as well as his conviviality and generosity as a teacher and colleague-have led to a constant stream of interesting and fruitful putting-togethers and rearrangements of heretofore disparate areas of logic and the theory of "rationality": proof theory and bounded arithmetic ( [54], [62]), temporal logic and social levels ( [63], [66], Bayesian probability theory and defeasible inference ( [1]), epistemic and dynamic epistemic logic ( [67], [69]), modal, deontic, and finite information logics ( [76]), [67], [53], [3]), belief revision theory, relevance and topology ( [8], [7], [64], [12]), electoral and political theory ( [52], [17]), and even literature and life ( [71], [73]). Juxtaposing these traditions of research with one another by asking philosophical questions yields interesting accounts of tensions and presuppositions among them.…”

Section: Introductionmentioning

confidence: 99%

Parikh and Wittgenstein

Floyd

2017

Outstanding Contributions to Logic

View full text Add to dashboard Cite

A survey of Parikh's philosophical appropriations of Wittgensteinian themes, placed into historical context against the backdrop of Turing's famous paper [104], "On computable numbers, with an application to the Entscheidungsproblem" and its connections with Wittgenstein and the foundations of mathematics. Characterizing Parikh's contributions to the interaction between logic and philosophy at its foundations, we argue that his work gives the lie to recent presentations of Wittgenstein's so-called metaphilosophy (e.g., [38]) as a kind of "dead end" quietism. From early work on the idea of a feasibility in arithmetic ([54]) and vagueness ([56]) to his more recent program in social software ([63]), Parikh's work encompasses and touches upon many foundational issues in epistemology, philosophy of logic, philosophy of language, and value theory. But it expresses a unified philosophical point of view. In his most recent work, questions about public and private languages, opportunity spaces, strategic voting, non-monotonic inference and knowledge in literature provide a remarkable series of suggestions about how to present issues of fundamental importance in theoretical computer science as serious philosophical issues.

show abstract

Finite information logic

Cited by 8 publications

References 8 publications

1. Setting the Stage

1. Setting the Stage

The Logic of Approximate Dependence

Parikh and Wittgenstein

Contact Info

Product

Resources

About