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The list of non-classical logic, as far as I can see, was initially supposed to be in order of properties of classical logic that are not satisfied. However, some non-classical logic are considered so also because they are syntactically different from classical logic (besides, S1-S5 are also mentioned as classical logics). I propose to reshape the list so that it has one item for family of non-classical logic. Paolo Liberatore (Talk) 16:28, 28 September 2005 (UTC)
Shouldn't Jaynes' model of probability theory as an extension of classical logic be included in the article? 220.127.116.11 02:00, 28 November 2005 (UTC)ragnar
Which non-classical logic denies commutativity of conjunction? Panu Kalliokoski
It would be useful to clarify what happens to arithmetic & algebra in the face of non-classical logics. Can one have non-classical arithmetic & algebra? Sholto Maud 11:02, 6 June 2006 (UTC)
- Because boolean algebra is two-valued. Simões (talk/contribs) 18:04, 28 October 2006 (UTC)
The situation with Boolean algebra is that it could mean either two-element Boolean algebra or any of the other Boolean algebras (note the plural). I've fixed the two-valued logic article though, so at least that is clear now. :-) Tijfo098 (talk) 11:59, 28 March 2011 (UTC)
- Nope, it's a Non-monotonic logic. Tizio 13:46, 16 May 2007 (UTC)
- Thanks, re-reading the article it is quite clear. Pgr94 14:30, 16 May 2007 (UTC)
Truth function, truth condition, bivalance
Modal logic is currently grouped among the non-classical logics. Kripkean modal logic does, however, satisfy the five conditions from the article, and admits a bivalent, truth-conditional semantics in terms of Kripke structures.
Likewise, there is an issue in interpreting predicate logic in terms of compositional truth conditions: is true when there is some t for which is true. But for the terms of the language is not, in general, a subformula of , so what is the truth function associated with supposed to be a truth function of? The simplicity of the T-schema for the quantifiers should not blind us to the fact that the quantifiers act on predicates, not propositions, and so are not the kind of thing that can be expressed as first-order functions on truth values.
And a last comment: the article talks of the five conditions, and of truth functions and bivalence, but does not discuss the relationship between them. And, in fact, I know of no work that relates them, though they are the kind of properties one needs for a Gödel-style completeness proof to yield a bivalent interpretation for the language.
I propose dropping talk of truth functions from the discussion of what a classical logic is in favour of truth conditions, calling (Kripkean) modal logic classical. And I'd be delighted if anyone could give more of a connection between the inferential and model-theoretic conditions for a logic to be classical; failing this we need to list the two side by side. And we need some discussion of the issues about when a many-valued logic can be considered classical or not. — Charles Stewart (talk) 09:04, 29 April 2009 (UTC)
- Perhaps a separate section is needed for those logics that contain the classical one as a fragment in some sense. But it would need to be sourced, not written off the top of the head. Tijfo098 (talk) 11:54, 28 March 2011 (UTC)
Removed two entries
I've removed two entries added by Jagged 85. I WP:AGF that he misunderstood "classical" to mean "old" or something like that, instead of the technical way in which it is used here. Tijfo098 (talk) 11:52, 28 March 2011 (UTC)
The introduction to the article contains a lot of jargon terminology, which is not even slightly understandable to the average reader. Please would someone with a talent for teaching and simplification re-write it in plain English ? Many thanks ! Darkman101 (talk) —Preceding undated comment added 23:03, 31 May 2013 (UTC)