V. Harnik, M. Makkai, Lambek's Categorical Proof Theory and Lauchli's Abstract Realizability, Journal of Symbolic Logic 57 (1992), pp. 200-230. Home/Search Document Not in Database Summary Related Articles Check |
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The Shuffle Hopf Algebra and Noncommutative Full Completeness - Blute, Scott (1996) (5 citations) (Correct)
....space, under pointwise operations. We call it the space of proofs associated to the sequent F F 0 . Note that we identify formulas with definable functors. Before obtaining a full completeness theorem, we first obtained a traditional completeness theorem, which is analogous to the results of [25, 20]. Theorem 2.9 (Completeness) Let M N be a balanced binary sequent. If the unique cutfree proof structure associated to M N is not a proof net for the theory MLL MIX, then Dinat(M; N) is a zero dimensional vector space. The key lemma in extending this result to a full completeness theorem ....
V. Harnik, M. Makkai, Lambek's Categorical Proof Theory and Lauchli's Abstract Realizability, Journal of Symbolic Logic 57 (1992), pp. 200-230.
Linear Läuchli Semantics - Blute, Scott (Correct)
....Formula = set with a distinguished permutation on it Proof = invariant element. A set with a distinguished permutation may be identified with a Z set (a set with an action of the free cyclic group Z) Thus, from this viewpoint, Lauchli s abstract models are nothing more than Z set models [23]. Lauchli s Completeness Theorem says: a formula is provable if and only if its interpretation in every abstract model contains an invariant element (i.e. an abstract proof ) Lauchli s semantics also has a categorical interpretation. The category of Z sets is a cartesian closed category ( ....
....proof ) Lauchli s semantics also has a categorical interpretation. The category of Z sets is a cartesian closed category ( ccc) and so interprets simply typed calculus as in [29] or equivalently deductions in a fragment of intuitionistic logic. A categorical presentation can be found in [23]. While Lauchli s semantics is a semantics of proofs, Lauchli s theorem is finally about provability, rather than genuine proofs. Thus, we might ask for a better result: can one find a notion of abstract model which characterizes proofs themselves This is the full completeness problem [2] From ....
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V. Harnik, M. Makkai, Lambek's Categorical Proof Theory and Lauchli's Abstract Realizability, Journal of Symbolic Logic 57, (1992), pp. 200-230.
Normalization and the Yoneda Embedding - Cubric, Dybier, Scott (Correct)
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V. Harnik and M. Makkai, Lambek's categorical proof theory and Lauchli's abstract realizability, J. Symbolic Logic 57 (1992), pp. 200-230.
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