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 Nominal sets (2)
 Enriched categories (1)
 Relation lifting (1)
 Duality (1)
 FraenkelMostowski sets (1)

 Cover modality (1)
 Corecursion (1)
 Dynamic Epistemic Logic (1)
 Infinitary lambda calculus (1)
 Intuitionistic Dynamic Epistemic Logic (1)
 Pointfree semantics (1)
 Intuitionistic modal logic (1)
 Commutative quantale (1)
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 Exact square (1)
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Articles 1  6 of 6
FullText Articles in Other Computer Engineering
Epistemic Updates On Algebras, Alexander Kurz, Alessandra Palmigiano
Epistemic Updates On Algebras, Alexander Kurz, Alessandra Palmigiano
Engineering Faculty Articles and Research
We develop the mathematical theory of epistemic updates with the tools of duality theory. We focus on the Logic of Epistemic Actions and Knowledge (EAK), introduced by BaltagMossSolecki, without the common knowledge operator. We dually characterize the product update construction of EAK as a certain construction transforming the complex algebras associated with the given model into the complex algebra associated with the updated model. This dual characterization naturally generalizes to much wider classes of algebras, which include, but are not limited to, arbitrary BAOs and arbitrary modal expansions of Heyting algebras (HAOs). As an application of this dual characterization, we ...
Dynamic Sequent Calculus For The Logic Of Epistemic Actions And Knowledge, Giuseppe Greco, Alexander Kurz, Alessandra Palmigiano
Dynamic Sequent Calculus For The Logic Of Epistemic Actions And Knowledge, Giuseppe Greco, Alexander Kurz, Alessandra Palmigiano
Engineering Faculty Articles and Research
"Dynamic Logics (DLs) form a large family of nonclassical logics, and perhaps the one enjoying the widest range of applications. Indeed, they are designed to formalize change caused by actions of diverse nature: updates on the memory state of a computer, displacements of moving robots in an environment, measurements in models of quantum physics, belief revisions, knowledge updates, etc. In each of these areas, DLformulas express properties of the model encoding the present state of affairs, as well as the pre and postconditions of a given action. Actions are semantically represented as transformations of one model into another, encoding the ...
Relation Lifting, With An Application To The ManyValued Cover Modality, Marta Bílková, Alexander Kurz, Daniela Petrişan, Jirí Velebil
Relation Lifting, With An Application To The ManyValued Cover Modality, Marta Bílková, Alexander Kurz, Daniela Petrişan, Jirí Velebil
Engineering Faculty Articles and Research
We introduce basic notions and results about relation liftings on categories enriched in a commutative quantale. We derive two necessary and sufficient conditions for a 2functor T to admit a functorial relation lifting: one is the existence of a distributive law of T over the “powerset monad” on categories, one is the preservation by T of “exactness” of certain squares. Both characterisations are generalisations of the “classical” results known for set functors: the first characterisation generalises the existence of a distributive law over the genuine powerset monad, the second generalises preservation of weak pullbacks.
The results presented in this paper ...
Nominal Coalgebraic Data Types With Applications To Lambda Calculus, Alexander Kurz, Daniela Petrişan, Paula Severi, FerJan De Vries
Nominal Coalgebraic Data Types With Applications To Lambda Calculus, Alexander Kurz, Daniela Petrişan, Paula Severi, FerJan De Vries
Engineering Faculty Articles and Research
We investigate final coalgebras in nominal sets. This allows us to define types of infinite data with binding for which all constructions automatically respect alpha equivalence. We give applications to the infinitary lambda calculus.
Nominal Regular Expressions For Languages Over Infinite Alphabets, Alexander Kurz, Tomoyuki Suzuki, Emilio Tuosto
Nominal Regular Expressions For Languages Over Infinite Alphabets, Alexander Kurz, Tomoyuki Suzuki, Emilio Tuosto
Engineering Faculty Articles and Research
We propose regular expressions to abstractly model and study properties of resourceaware computations. Inspired by nominal techniques – as those popular in process calculi – we extend classical regular expressions with names (to model computational resources) and suitable operators (for allocation, deallocation, scoping of, and freshness conditions on resources). We discuss classes of such nominal regular expressions, show how such expressions have natural interpretations in terms of languages over infinite alphabets, and give Kleene theorems to characterise their formal languages in terms of nominal automata.
Nominal Computation Theory (Dagstuhl Seminar 13422), Mikołaj Bojanczyk, Bartek Klin, Alexander Kurz, Andrew M. Pitts
Nominal Computation Theory (Dagstuhl Seminar 13422), Mikołaj Bojanczyk, Bartek Klin, Alexander Kurz, Andrew M. Pitts
Engineering Faculty Articles and Research
This report documents the program and the outcomes of Dagstuhl Seminar 13422 “Nominal Computation Theory”. The underlying theme of the seminar was nominal sets (also known as sets with atoms or FraenkelMostowski sets) and they role and applications in three distinct research areas: automata over infinite alphabets, program semantics using nominal sets and nominal calculi of concurrent processes.