J. M. Dunn, Conseqution formulation of positive R with co-tenability and t, in [3]. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
The Logic of Bunched Implications - O'Hearn, Pym (1999) (15 citations) (Correct)
....are possible for ; but not for , The introduction rules then become #, # # # # # # ## and #; # # # # # # # # . In this scheme, the antecedents are no longer sequences, but are trees with propositions as leaves and internal nodes labelled by , or ; or in short, bunches [13, 6, 36]. Aside: We have chosen to use a di#erent symbol, #, for the multiplicative implication, in order to avoid confusion with #. Although many of the formal properties in the multiplicative connectives are the same, the way that they mesh with additive connectives gives rise to di#erent behaviour. ....
....is beyond the scope of this introductory article; the details of predicate BI can be found in [33] 1.3. The significance of BI. We must emphasize that the tools used to define and analyze BI have been available for some time. For one, bunches have been used in sequent calculi for relevant logics [13]; the mere fact of existence of a logic like BI would come as no surprise to relevantists. For another, many of the categorical fundamentals of BI had, with the benefit of hindsight, already been laid down even earlier, in a classic paper of Day [10] One of our main aims here is to stress the ....
J. M. Dunn, Conseqution formulation of positive R with co-tenability and t, in [3].
The Logic of Bunched Implications - O'Hearn, Pym (1999) (15 citations) (Correct)
.... for ; but not for , The introduction rules then become Gamma ; Gamma Gamma and Gamma ; Gamma In this scheme, the antecedents are no longer sequences, but are trees with propositions as leaves and internal nodes labelled by , or ; or in short, bunches [15, 6, 37]. Aside: We have chosen to use a different symbol, Gamma , for the multiplicative implication, in order to avoid confusion with Gammaffi . Although many of the formal properties in the multiplicative connectives are the same, the way that they mesh with additive connectives gives rise to ....
....is beyond the scope of this introductory article; the details of predicate BI can be found in [34] 1.3 The Significance of BI We must emphasize that the tools used to define and analyze BI have been available for some time. For one, bunches have been used in sequent calculi for relevant logics [15]; the mere fact of existence of a logic like BI would come as no surprise to relevantists. For another, many of the categorical fundamentals of BI had, with the benefit of hindsight, already been laid down even earlier, in a classic paper of Day [10] One of our main aims here is to stress the ....
J.M. Dunn. Conseqution formulation of positive R with co-tenability and t. In [3], pp381--391.
Logic Programming with Bunched Implications (Extended Abstract) - Pym (Correct)
.... on the distinction between , and ; We stipulate that Contraction and Weakening are possible for ; but not for , In this scheme, the antecedents are no longer sequences, but are trees with leaves labelled with propositions and internal nodes labelled by , or ; or in short, bunches [5,2,22]. 2 Propositional BI 2.1 A Natural Deduction Presentation In this section, we give a presentation of BI in sequential natural deduction form, i.e. a sequent presentation based on introduction and elimination rules. We call the system NBI. A sequent calculus presentation (LBI) can be found in ....
J.M. Dunn. Conseqution formulation of positive R with co-tenability and t. In
On Bunched Predicate Logic - Pym (1999) (14 citations) (Correct)
.... for ; but not for , The introduction rules then become Gamma ; OE Gamma OE Gamma and Gamma ; OE Gamma OE The antecedents are no longer sequences; rather, they are trees with propositions as leaves and internal nodes labelled with , or ; or in short, bunches [10, 6, 27]. It is all very well to postulate proof rules in this way, but what meaning or significance, if any, does the resulting logic have We argue herein that BI possesses two very natural semantics. The first, a BHK style semantics of the proof theory, arises from doubly closed categories (DCCs) in ....
J.M. Dunn. Conseqution formulation of positive R with co-tenability and t. In [3], 381--391.
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