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- 1 Next tasks
- 2 Improve logic article
- 3 Article composition
- 4 Tasks for sometime: logic
- 5 Tasks for sometime: &c
- Create Vending machine (process theory), cf. Process theory -- Jun 2009
- Linear logic - semantics section, Hopf algebra and [Category Theory for Linear Logicians http://www.site.uottawa.ca/~phil/papers/catsurv.web.pdf] -- Jul 2009
- Second-order logic: change talk of standard semantics to set-theoretic semantics, and contrast to the dependence of Henkin semantics on simply-typed lambda-calculus -- Apr 2009
- Another round of surgery on Paradoxes of material implication, see Talk:Paradoxes of material implication. -- Mar 2009
- Add discussion of fan theorem to bar induction, cf. Rathjen -- Mar 2009
- Alasdair Macintyre: fact check londonsocialisthistorians.org, look for other accts. Mar 2009
- Sort out intensional logic, start Imre Rusze (obit), ask User:Physis -- May 2009
- Add institute to Robert von Ostertag -- May 2009
The road to rating FA
- Create logic article outline based on User:Renamed user 4/logic and current section headings -- Mar 2009
Reconcile lede's, ref Definitions of logic
- Merge current controversies into Db's semantics section
- Put in new inference section
- FA process, attempt 2
- Deal with comments at Wikipedia:Peer review/Logic/archive1 -- Jan 2006
- Straight to FA, or via GA?
- Fix computational redlinks: Logics and meanings of programs, Mathematical logic and formal languages,
Arithmetic and logic structures-- 27 Oct 2005
- Integrate Trivium into logic, subsection informal reasoning, maybe logic as an art of thinking (Sister Miriam Joseph) -- Feb 2009
- The History of logic section is broken:
- Two most important facts about HoL are (i) the Aristotelian tradition has had the greatest impact on the subject today, and (ii) the transmission from ancient to modern times was crucially intermediated by Islamic scholarship.
- Chinese logic, to great extent, and Indian logic, to a lesser extent, get more coverage than their relatively slight impact on modern thinking can justify. These points are for more specialist articles.
- The most important commentator on Indian logic for the purposes of the article is Colebrooke's Philosophy of the Hindus, which is, of course, not mentioned, though two less influential commentators are. -- Mar 2009
- Troelstra, 1992, Hist. of constructivisms in C20th: talks of 4 schools, success of Bishop's school 'winning'.
- Terwijn, 2006, Constructive logic and the Medvedev lattice
- Kolmogorov, 1932, 'On the interpretation of intuitionistic logic'
- Yuri Medvedev, 1955, 'Degrees of difficulty of mass problems' (Doklady Akademii Nauk SSSR, 104/4:501--504),
- Yuri Medvedev, 1962, 'Finite problems' (Doklady Akademii Nauk SSSR, 142:1015--1018)
- Sort out mess per Talk:Hilbert system
- Integrate discussion of key applications of HSs:
- equational logic & quantification per Basic formal equational predicate logic, and interaction with Uniform Substitution
- Modal logic & Hilbert-Lewis systems
- "Natural" deduction, based on metarules
- Integrate discussion of Hilbert's finitism into Hilbert's second problem, based on (Zach 2009). -- Feb 2009
- Improve discussion in finitism -- Feb 2009
- Key figures before Tarski: Alexander Bain, George Boole, Hugh MacColl, Ernst Schröder, Charles S. Pierce, Christine Ladd-Franklin, William Stanley Jevons, John Venn, Platon Sergeevich Poretskii, John Stuart Mill, Robert Grassmann
- Merge Boole's syllogistic into LoT. Points from Talk:Boole's syllogistic:
- Boole did not propose a separate syllogistic calculus, rather what he proposed was an interpretation of syllogistic into his algebra. There are a few accounts of the interpretation on the web, of which (Burris 2001) is perhaps the best.
- The current article is talking about how this interpretation proposes a resolution to the problem of existential import (see square of opposition), one incompatible with Aristotle assertions. One of the many problems with the article as it stands is that it isn't clear that that is what it is doing. I suppose no one else is going to fix it but me: I'll get around to it...
- Naturally this calculus is propositional logic and not predicate logic. The embedding of syllogistic into propositional logic shows that syllogistic corresponds to a very weak fragment of predicate logic.
- Boole, G. (1850). Gutenberg text of Laws of Thought
- Burris, Stanley (2000). The Laws of Boole's Thought.
- Burris, Stanley (2001). A Fragment of Boole's Algebraic Logic Suitable for Traditional Syllogistic Logic.
- Hailperin, T. (1976/1986). Boole's Logic and Probability. North Holland.
- Hailperin, T. (1981). Boole’s algebra isn’t Boolean algebra. Mathematics Magazine 54:172–184. Reprinted in A Boole Anthology, ed. by James Gasser. Synthese Library volume 291. Springer 2000.
- Stanley Burris' bibliography on the history of mathematical logic.
- Maria Manzano (2005). Extensions of first-order logic. In Cambridge Tracts in Theoretical Computer Science 19, CUP.
- Meinke & Tucker's "Many Sorted Logic and Its Applications"
- John Tucker's post on FOM on the reduction of many-sorted to first-order logic.
- Farm out Stoic logic from history of logic
- Summarise Sect 3.5 of SEP:lvon-warsaw Lukasiewicz on Stoic logic as a system of rules, and section 3.3 on bivalence.
Tasks for sometime: logic
- Do something about the mess in validity and soundness --- 28 Oct 2004
- Mass and count constructons needed in Quantification ---- 20 Nov 2004
- Sort out Principle of bivalence -- Mar 2009
- Hartman's "The Structure of Value", axiom of value;
- Rebuschi (2008). Czeżowski's axiological concepts as full-fledged modalities:
- Literary section on logic (date=June 2009)
- Kripke semantics: canonical model constructions due to (Makinson 1970) "On some completeness theorems in modal logic"
- Neighbourhood models
- Add pages subformula property -- 18 Aug 2004
Semantics & MSfS
- Integrate overlap between game semantics, logical argument, and semantics of logic ---- 30 Aug 2004
- Geometric logic, Boolean relation theory, Stone spaces, and Equilogical spaces ---- 17 Nov 2004
- Equational logic, order-sorted logic, and rewriting logic ---- 7 Dec 2004
- Make list of logic articles of joint concern to maths & philosophy, reply to GregBard -- Feb 2009
- Start with: modal logic, predicate logic, soundness, completeness, Hilbert system
- What standards do we want for these articles? How about elementary formal reasoning, sufficient for detailed discussion of soundness theorem & deduction theorem, but not as much as needed for completeness theorem?
Tasks for sometime: &c
- Raph Levien: incorporate material on remailers (see talk) --- Mar 2007
- In order to show that the axioms of the class of algebras we consider capture exactly the collection of predicates we have in mind, a representation theorem is necessary. A representation theorem is a correspondence between an abstract algebra and its set-theoretical model. The first representation theorem is due to Cayley [Cay78] showing that every abstract group is isomorphic to a concrete group of permutations. A representation theorem for the algebra of all predicates was first proved by Lindenbaum and Tarski [Tar35]. They proved that a Boolean algebra is isomorphic to the collection of all subsets of some set if and only if it is complete and atomic. This general result restricts the class of Boolean algebras for which a concrete representation exists. It was Stone [Sto36] who first saw a connection between algebra and topology. He constructed from a Boolean algebra a set of points using prime ideals which can be made into a topological space in a natural way. Conversely, using a topology on a set of points he was able to construct a Boolean algebra. For certain topological spaces (later called Stone spaces) these constructions give an isomorphism. In a later paper [Sto37], Stone generalized this correspondence from Stone spaces to spectral spaces and from Boolean algebras to distributive lattices. Hofmann and Keimel [HK72] described the Stone representation theorem in a categorical framework showing a duality between the category of Boolean algebras and a sub-category of topological spaces. A representation theorem for Boolean algebras with operators has been considered by J'onsson and Tarski [JT51, JT52]. By means of an extension theorem they proved that operators on a Boolean algebra can be naturally extended to completely additive operators on a complete and atomic Boolean algebra.
- Stone's representation theorem leaves open the problem of finding an abstract characterization of topological spaces. For every topological space, its lattice of open sets forms a frame. This fact leads Papert and Papert [PP58] to a representation theorem between spatial frames and sober spaces. Even further, Isbell [Isb72a] gives an adjunction between the category of topological spaces with continuous functions and the opposite category of frames with frame homomorphisms. This adjunction yields a duality between the category of sober spaces and the category of spatial frames.
- LISPy things:
- LISP macro systems: namespace issues from RPG's Technical Issues of Separation paper, history of macros (MacLisp, etc.), CL macros (DEFMACRO, FLET), Hygiene (Kohlbecker's algorithm, syntactic closures, macros that work, R4RS syntax-rules, syntax-case) ---- 15 Dec 2004
- LISP object systems: message passing vs. generic functions, MOPs (see list of current MOPs), Flavors, CommonLOOPS, RPG's CLOS paper Alex Shinn's summary, SICP objects are closures approach, scheme object systems (see CMU Scheme OO directory), Dylan's object system (see Kidd's tutorial, multiple inheritance superclass linearization proposal, compilation issues ---- 15 Dec 4004