Results 1 
7 of
7
Categorical Proof Theory of CoIntuitionistic Linear Logic
"... Summary. To provide a categorical semantics for cointuitionistic logic, one has to face the fact, noted by Tristan Crolard, that the definition of coexponents as adjuncts of coproducts does not work in the category Set, where coproducts are disjoint unions. Following the familiar construction of ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
(Show Context)
Summary. To provide a categorical semantics for cointuitionistic logic, one has to face the fact, noted by Tristan Crolard, that the definition of coexponents as adjuncts of coproducts does not work in the category Set, where coproducts are disjoint unions. Following the familiar construction of models of intuitionistic linear logic with exponent!, we build models of cointuitionistic logic in symmetric monoidal closed categories with additional structure, using a variant of Crolard’s term assignment to cointuitionistic logic in the construction of a free category. 1
hypotheses, conjectures and expectations. Rough set semantics and prooftheory
 Advances in Natural Deduction
, 2013
"... Summary. In this paper biintuitionism is interpreted as an intensional logic which is about the justification conditions of assertions and hypotheses, extending C. Dalla Pozza and C. Garola’s pragmatic interpretation [18] of intuitionism, seen as a logic of assertions according to a suggestion by M ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
Summary. In this paper biintuitionism is interpreted as an intensional logic which is about the justification conditions of assertions and hypotheses, extending C. Dalla Pozza and C. Garola’s pragmatic interpretation [18] of intuitionism, seen as a logic of assertions according to a suggestion by M. Dummett. Revising our previous work on this matter [5], we consider two additional illocutionary forces, (i) conjecturing, seen as making the hypotheses that a proposition is epistemically necessary, and (ii) expecting, regarded as asserting that a propostion is epistemically possible; we show that a logic of expectations justifies the double negation law. We formalize our logic in a calculus of sequents and study bimodal Kripke semantics of biintuitionism based on translations in S4. We look at rough set semantics following P. Pagliani’s analysis of “intrinsic coHeyting boundaries ” [40] (after Lawvere). A Natural Deduction system for cointuitionistic logic is given where proofs are represented as upside down Prawitz trees. We give a computational interpretation of cointuitionism, based on T. Crolard’s notion of coroutine [16] as the programming construction corresponding to subtraction introduction. Our typed calculus of coroutines is dual to
On the π calculus and distributed calculi for cointuitionistic logic, conference paper presented at the LAMCONCUR’11 Workshop
, 2011
"... logic ..."
concurrency and
"... IOS Press On the πcalculus and cointuitionistic logic. Notes on logic for ..."
Abstract
 Add to MetaCart
IOS Press On the πcalculus and cointuitionistic logic. Notes on logic for
2 A Critique of the Foundations of Hoare Style Programming Logics
"... Certification de programmes impératifs d’ordre supérieur avec mécanismes de contrôle ..."
Abstract
 Add to MetaCart
Certification de programmes impératifs d’ordre supérieur avec mécanismes de contrôle
CERTIFICATE OF APPROVAL
, 2014
"... To my lovely wife, Jenny Eades. ii Program testing can be used to show the presence of bugs, but never to show their absence! –Dijkstra (1970) iii ACKNOWLEDGEMENTS The first person I would like to acknowledge is my advisor Aaron Stump. He is one of the kindest and most intelligent people I have had ..."
Abstract
 Add to MetaCart
(Show Context)
To my lovely wife, Jenny Eades. ii Program testing can be used to show the presence of bugs, but never to show their absence! –Dijkstra (1970) iii ACKNOWLEDGEMENTS The first person I would like to acknowledge is my advisor Aaron Stump. He is one of the kindest and most intelligent people I have had the pleasure to work with, and without his guidance I would have never made it this far. I can only hope to acquire the insight and creativity you have when working on a research problem. Furthermore, I would like to thank him for introducing me to my research area in type theory and the foundations of functional programming languages. Secondly, I would like to thank my wife, Jenny Eades, whose hard work literally made it possible for there to be food on our table and a roof over our heads. She