Kobayashi, S. (1997). Monad as modality. Theoretical Computer Science, 175:29--74. Home/Search Document Not in Database Summary Related Articles Check |
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A Judgmental Reconstruction of Modal Logic - Pfenning, Davies (2001) (1 citation) (Correct)
....the decomposition of the lax modality fl A as 32A and lax implication A ) B as (2A) oe B. Through a computational interpretation of proofs in modal logic we further obtain a new formulation of Moggi s monadic metalanguage (Moggi, 1998; 1989; 1991) combining and systematizing previous work by S. Kobayashi (1997) and Benton, Bierman, and de Paiva (1998) At the level of judgments, the above development requires surprisingly few primitive notions. In particular, we only need hypothetical judgments to explain implication, and categorical judgments to explain the modalities. We have thus obtained a ....
....a simultaneous substitution, either in the syntax or in the side condition. 4.3. Axiomatic Characterization Necessity can be characterized axiomatically by the inference rule of necessitation A true nec 2A true together with the following three axioms (see, for example, Vigan o, 1997; Kobayashi, 1997; Alechina et al. 1998) 2(A oe B) oe(2A oe 2B) true 2A oe A true 2A oe 22A true A Judgmental Reconstruction of Modal Logic 11 The derivations of these axioms in natural deduction is given in Section 6 in abbreviated form as proof terms. 5. Possibility We may view hypotheses A 1 ....
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Kobayashi, S. (1997). Monad as modality. Theoretical Computer Science, 175:29--74.
Relating Categorical and Kripke Semantics for.. - Alechina, de Paiva.. (1998) (1 citation) (Correct)
..... B 3B (3 I ) 2A 1 Delta Delta Delta 2An B] 2A 1 : 2An 3B 3C 3C (3 E ) Figure 2: Natural Deduction rules for Constructive S4 of this system, which enforces the equiprovability between falsum and possibly falsum was described by Kobayashi in (Kobayashi 1997). The second system of modal logic we shall consider is called CL (for Curry Logic , or Computational Logic ) It is obtained by adding to the axioms of intuitionistic propositional logic the axioms T and 4 above and the strength axiom: S (A B) 3A 3B) This system also has a ....
....monad. These models were in fact the original motivation for Moggi s computational lambda calculus and CL can be seen as reverse engineering from that (Benton et al. 1998) Hence we refrain from stating categorical soundness and completeness for this system, but of course they hold as expected (Kobayashi 1997). 7 Conclusions This paper shows how traditional Kripke semantics for two systems of intuitionistic modal logic can be related via duality theory to the categorical semantics of (natural deduction) proofs for these logics. Duality theorems establish a connection between Kripke models and modal ....
Kobayashi, S. 1997. Monad as modality. Theoretical Computer Science 175:29 -- 74.
Under consideration for publication in Math. Struct. in .. - Judgmental.. (Correct)
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Kobayashi, S. (1997). Monad as modality. Theoretical Computer Science, 175:29--74.
A Modal Analysis of Staged Computation - Rowan Davies And (1996) (124 citations) (Correct)
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Kobayashi, S. 1997. Monad as modality. Theoretical Computer Science 175, 29--74.
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