, Onweak completeness of intuitionistic predicate logic, The Journal of Symbolic Logic, vol. 27 (1962), pp. 139--158. Home/Search Document Not in Database Summary Related Articles Check |
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The Undecidability of lambda-Definability - Loader (Correct)
.... Undecidability of Definability Ralph Loader, Oxford University Introduction In this article, we shall show that the Plotkin Statman conjecture [4, 7] is false. The conjecture was that, in a model of the simply typed calculus with only finitely many elements at each type, definability (by a closed term of the calculus) is decidable. This conjecture had been shown to imply many things, for example, Statman [7] see also Wolfram s book [8] has ....
....the Plotkin Statman conjecture [4, 7] is false. The conjecture was that, in a model of the simply typed calculus with only finitely many elements at each type, definability (by a closed term of the calculus) is decidable. This conjecture had been shown to imply many things, for example, Statman [7] (see also Wolfram s book [8] has shown it implies the decidability of pure higher order pattern matching (a problem that remains open at the time of writing) and is equivalent to higher order pattern matching with ffi functions. The proof of undecidability given here uses encodings of semi Thue ....
R. Statman. Completeness, invariance, and -definability. Journal of Symbolic Logic, 47(1), pages 17--26, 1982.
The Logic of Provability - Japaridze, de Jongh (1998) (13 citations) (Correct)
.... the original proofs by de Jongh and Sambin (see Sambin [1976] Smory nski [1978,1985] and, for the first proof of uniqueness, Bernardi [1976] many other, different, proofs have been given for the fixed point theorems, syntactical as well as semantical ones, the latter e.g. in Gleit and Goldfarb [1990]. It is also worthwhile to remark that theorem 4.3 follows from theorem 4.1 (which can be seen as a kind of implicit definability theorem) by way of Beth s definability theorem that holds for L. The latter can be proved from interpolation in the usual manner. Interpolation can be proved ....
....essentially reflexive. At the same time no consistent finite(ly axiomatized) theory which satisfies the conditions of Godel s second incompleteness theorem can even be locally essentially reflexive, for otherwise such a theory would prove its own consistency. In fact, it is shown in Visser [1990] that essential reflexivity is equivalent to full induction. The idea of the proof, by the way, is already present in Kreisel and L evy [1968] That local essential reflexivity is much weaker than global essential reflexivity follows from the following observation. For any reasonable theory T , ....
[Article contains additional citation context not shown here]
Finite Kripke models and predicate logics of provability, Journal of Symbolic Logic, 55, pp. 1090--1098. A. Avron
A Software Architecture for Knowledge-Based Systems - Fensel, Groenboom (1999) (Correct)
....(MLPM [Fensel Groenboom, 1996] Each of these languages are variants of dynamic logic. Dynamic logic [Harel, 1984] was developed to express states, state transitions, and procedural control of these transitions in a logical framework. Dynamic logic uses the possible worlds semantics of [Kripke, 1959] for this purpose. A state is represented by a possible world through the value assignments of the program variables. MCL extends the representation of a state. A state is represented by an algebra following the states asalgebras paradigm of abstract state machines [Gurevich, 1994] A state ....
S.A. Kripke: A Completeness Theorem in Modal Logic, Journal of Symbolic Logic, 24:1---14, 1959.
The Logic of Provability - Japaridze, de Jongh (1997) (13 citations) (Correct)
.... L B A(B) After the original proofs (see Sambin [1976] Smory nski [1978,1985] and, for the first proof of uniqueness, Bernardi [1976] many other, different, proofs have been given for the fixed point theorems, syntactical as well as semantical ones, the latter e.g. in Gleit and Goldfarb [1990]. It is also worthwile to remark that theorem 4.3 follows from theorem 4.1 (which can be seen as a kind of implicit definability theorem) by way of Beth s definability theorem that holds for L. The latter can be proved from interpolation in the usual manner, and interpolation can be proved ....
....essentially reflexive. At the same time no consistent finite(ly axiomatized) theory which satisfies the conditions of Godel s second incompleteness theorem can even be locally essentially reflexive, for otherwise such a theory would prove its own consistency. In fact, it is shown in Visser [1990] that essential reflexivity is equivalent to full induction. The idea of the proof, by the way, is already present in Kreisel and L evy [1968] That local essential reflexivity is much weaker than global essential reflexivity follows from the folowing observation. For any reasonable theory T , T ....
[Article contains additional citation context not shown here]
Finite Kripke models and predicate logics of provability, Journal of Symbolic Logic, 55, pp. 1090--1098. A. Avron
Decidability and Finite Model Property of Substructural Logics - Ono (1998) (3 citations) (Correct)
....is not simpler than the lower one. Moreover it seems to be unable to estimate in advance how many times the contraction rule will be applied in the proof. Thus, there would be no way of telling when the construction of proof search trees eventually terminate. To overcome this difficulty, Kripke in [15] introduced the notion of cognate sequents and showed that it is enough to search for only proof search trees without redundant branches and under this restriction the above algorithm will eventually terminate. See e.g. 7] for the details. The key of the above proof is a result, called ....
S.A. Kripke, The problem of entailment ( abstract ), Journal of Symbolic Logic 24 (1959), 324.
Modal Change Logic (MCL): Specifying the Reasoning of .. - Fensel, Groenboom.. (1998) (1 citation) (Correct)
....First, we put MCL in the perspective of multimodal dynamic logics. Modal logic is an extension of (propositional or predicate) logic with the unary sentential operator , where A 15 traditionally has the informal meaning it is necessary that A. An early reference is [Lewis Langford, 1932] In [Kripke, 1959], Kripke developed the possible worlds semantics, according to which the formula A is true in some world w iff A holds in all worlds that are accessible from w via the relation R. There are many modal logics, each corresponding with a particular class of accessibility relations: e.g. the logic ....
S.A. Kripke: A Completeness Theorem in Modal Logic, Journal of Symbolic Logic, 24:1---14, 1959.
Explicit Provability And Constructive Semantics - Artemov (2001) (1 citation) Self-citation (Logic) (Correct)
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, Onweak completeness of intuitionistic predicate logic, The Journal of Symbolic Logic, vol. 27 (1962), pp. 139--158.
A simple proof of a theorem of Statman - Mairson (1992) (13 citations) Self-citation (Statman) (Correct)
....j x : oe:y : oe:x : Bool. 3. 4 Remarks on separation theorems in calculus It is instructive to realize how the notion of nonrecursive in the context of untyped calculus functions precisely in the same manner as the notion of non Kalmar elementary functions in the first order typed calculus [Sta82]. Scott s undecidability theorem (see, e.g. HS86] states that no two nonempty, disjoint sets of terms are recursively separable: given such sets and of terms closed under fij equality, no algorithm can decide, given an arbitrary x chosen from [ whether x 2 , or x 2 . Statman s Theorem ....
....a term coding an expression E in higher order type theory. Then E a b is fij equivalent to a if E is true, and to b if E is false. Hence deciding membership of E a b in or is as hard as deciding the truth of E, which cannot be computed in elementary time. Statman gives as well another corollary [Sta82]. Let be a set of terms of fixed type , closed under fij equality, where membership in is decidable in elementary time. Then contains all or none of the terms of type . The proof is trivial: suppose by contradiction that is nonempty, yet there exists a term b of type not in . Let be the ....
R. Statman. Completeness, invariance, and -definability. Journal of Symbolic Logic 47:1, 1982, pp. 17--26.
Simple Consequence Relations - Avron (1991) (60 citations) (Correct)
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Kripke S., The Problem of Entailment (abstract), Journal of Symbolic Logic, vol. 24 (1959), p. 324.
The Discovery Of My Completeness Proofs - Henkin (1996) (4 citations) (Correct)
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, Completeness in the theory of types, The Journal of Symbolic Logic, vol. 15 (1950), pp. 81--91.
Models of Lambda Calculi and Linear Logic: Structural, Equational .. - Loader (1994) (8 citations) (Correct)
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R. Statman. Completeness, invariance, and -definability. Journal of Symbolic Logic, 47(1), pages 17--26, 1982.
The Method of Hypersequents in the Proof Theory of Propositional.. - Avron (1994) (25 citations) (Correct)
No context found.
Kripke S., The Problem of Entailment (abstract), Journal of Symbolic Logic, vol. 24 (1959), p. 324. 35
Change of Belief in SKL Model Frames (Automatization.. - Alvarado, Núnez (1996) (Correct)
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S. Kripke: A completness theorem in modal logic. The Journal of Symbolic Logic. 24 - 1 (1959) pp. 1-14.
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