Bistructures, Bidomains and Linear Logic
نویسندگان
چکیده
Bistructures are a generalisation of event structures to represent spaces of functions at higher types; the partial order of causal dependency is replaced by two orders, one associated with input and the other output in the behaviour of functions. Bistructures form a categorical model of Girard’s classical linear logic in which the involution of linear logic is modelled, roughly speaking, by a reversal of the roles of input and output. The comonad of the model has associated co-Kleisli category which is equivalent to a cartesian-closed full subcategory of Berry’s bidomains.
منابع مشابه
Stable Bistructure Models of PCF
Stable bistructures are a generalisation of event structures to represent spaces of functions at higher types; the partial order of causal dependency is replaced by two orders, one associated with input and the other output in the behaviour of functions. They represent Berry’s bidomains. The representation can proceed in two stages. Bistructures form a categorical model of Girard’s linear logic...
متن کاملOn dialogue games and coherent strategies
We explain how to see the set of positions of a dialogue game as a coherence space in the sense of Girard or as a bistructure in the sense of Curien, Plotkin and Winskel. The coherence structure on the set of positions results from a Kripke translation of tensorial logic into linear logic extended with a necessity modality. The translation is done in such a way that every innocent strategy defi...
متن کاملStrategies as Profunctors
A new characterization of nondeterministic concurrent strategies exhibits strategies as certain discrete fibrations—or equivalently presheaves—over configurations of the game. This leads to a lax functor from the bicategory of strategies to the bicategory of profunctors. The lax functor expresses how composition of strategies is obtained from that of profunctors by restricting to ‘reachable’ el...
متن کاملFrom Strategies to Profunctors
A lax functor from a bicategory of very general nondeterministic concurrent strategies on concurrent games to the bicategory of profunctors is presented. The lax functor provides a fundamental connection between two approaches to generalizations of domain theory to forms of intensional domain theories, one based on game and strategies, and the other on presheaf categories and profunctors. The l...
متن کاملLinear Formulas in Continuous Logic
We prove that continuous sentences preserved by the ultramean construction (a generalization of the ultraproduct construction) are exactly those sentences which are approximated by linear sentences. Continuous sentences preserved by linear elementary equivalence are exactly those sentences which are approximated in the Riesz space generated by linear sentences. Also, characterizations for linea...
متن کامل