|WikiProject Mathematics||(Rated Start-class, Low-priority)|
|WikiProject Philosophy||(Rated Start-class, Low-importance)|
I'm pretty sure that Japardidze was not the first to propose games as foundational entities: its rather the point of Ludics (the new approach to linear logic that doesn't yet have a wikipedia entry, no doubt because no-one who knows enough about it and cares enough to write an entry has enough courage to put their name to a summary...), and also there's a not-so-new article by Walter Felscher proposing dialog games as a foundation for constructivism. ---- Charles Stewart 16:45, 18 Aug 2004 (UTC)
This article is a bit stub-like; it could be improved, I think, by a a simple example of a sentence (say of epsilon-delta analysis; something with some nice alternating quantifiers) and the corresponding game, just to give the reader an idea how the basic idea might work. I'll have a think, & try to have a go; though if anyone else is keen, please do. (As to Ludics: you could write an entry and not put your name to it....) --- Anon, 16.III.05
Lorenzen and Hintikka were not the only people active in this area in the 1960s. In addition, a major boost to the game turn in formal logic was the influential work of the Australian philosopher and computer pioneer, Charles Hamblin, in reviving dialogue games to analyse the so-called logical fallacies, such as circular arguments. A full treatment would also note that dialog games were first described by Aristotle, and were the main means of doing philosophy in the Middle Ages. Peirce's work in the 19th century also explored a game semantics for logical syntaxes.
In addition, including only a reference to the paper by Erik C. W. Krabbe is perhaps a little disengenuous. The same volume includes a paper by Wilfrid Hodges offering a sceptical account of the role of game semantics as a semantics for logical syntax. The papers preceeded a debate between the two authors.
Wilfrid Hodges: Dialogue Foundations: A Sceptical Look. The Aristotelian Society, Supplementary Volume LXXV, 2001, pp. 17-32.
-- Peter McBurney, Liverpool, 05.VIII.05.
The article is currently saying that the principle of compositionality fails, without being very specific. However, Hodges seems to have found a compositional semantics for IF logic. Can anyone fix this tension? (i.e. "tension" is weaker than "inconsistency")?
from the article on IF logic: "One cannot simply extend standard Tarskian semantics of FOL to accommodate IF logic. In fact, Hintikka claimed that a compositional semantics of IF logic would not be possible. However, Wilfrid Hodges has found such a semantics. [Hodges 1997]
Guslacerda 17:37, 9 August 2005 (UTC);
Is there any reason why the German is included at the head of this article? I might be missing something, but I don't see how game semantics are inherently German. --Perryar 16:45, 24 July 2007 (UTC)
From intuitionism to constructivism
I too have read Hintikka's claim that Charles Peirce anticipated game theoretic semantics. That Lorenzen originated such semantics to make sense of intuitionist logic is interesting. That mathematical constructivism can be given a game theoretic justification is downright exciting, at least if you believe, as I do, that constructivism is a promising research programme. Finally, Hodges's skepticism about this whole enterprise gives one pause; Hodges has peers but no superiors among living math logicians. Philip Meguire.
Game semantics, dialogic semantics, game theoretic semantics and ludics?
It seems to me that, at the moment, this page mentions a number of different approaches to semantics which have relatively little in common, except using game theoretical techniques in some way. Perhaps it could be useful if each one of these subject was given its own page instead? --Pietro Galliani (talk) 16:55, 9 March 2011 (UTC)