Petri Place/Transition (PT) nets are one of the most widely used models of concurrency. However, they still lack, in our view, a satisfactory semantics: on the one hand the \token game" is too intensional, even in its more abstract interpretations in term of nonsequential processes and monoidal categories; on the other hand, Winskel's basic unfolding construction, which provides a coreeection b...

2 Technical background 4 2.1 Martin-Löf Type Theory . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.1 Intuition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.2 Kinds of judgments . . . . . . . . . . . . . . . . . . . . . . 7 2.1.3 Rules for context formation and substitution . . . . . . . 8 2.1.4 Congruence rules for definitional equality . . . . . . . . . 9 2.1.5 Rules for ...

Eklund et al. (2002) present a graphical technique aimed at simplifying the verification of various category-theoretic constructions, notably the composition of monads. In this note we take a different approach involving string rewriting. We show that a given tuple (T,μ, η) is a monad if and only if T is a terminal object in a certain category of strings and rewrite rules, and that this fact ca...

As they can travel long distances, free space optical quantum states are good candidates for carrying information in quantum information technology protocols. These states, however, are often complex to produce and require protocols whose success probability drops quickly with an increase of the mean photon number. Here we propose a new protocol for the generation and growth of arbitrary states...

This paper defines a new proofand category-theoretic framework for classical linear logic that separates reasoning into one linear regime and two persistent regimes corresponding to ! and ?. The resulting linear/producer/consumer (LPC) logic puts the three classes of propositions on the same semantic footing, following Benton’s linear/non-linear formulation of intuitionistic linear logic. Seman...

We extend the theory of (co-)spans as a means of providing an algebraic approach to complex interactions as they arise in software-intensive systems. In order to make interconnections independent of the nature of components involved, interaction protocols are formalised not in terms of morphisms (i.e. part-of relationships) but a generalised notion of (co-)span in which the arms are structured ...

employing the notions of the strong $l$-topology introduced by zhangand the $l$-frame introduced by yao  and the concept of $l$-enrichedtopological system defined in the present paper, we constructadjunctions among the categories {bf st$l$-top} of strong$l$-topological spaces, {bf s$l$-loc} of strict $l$-locales and{bf $l$-entopsys} of $l$-enriched topological systems. all of theseconcepts are ...

The classical account for systematicity of human cognition supposes: (1) syntactically compositional representations; and (2) processes that are sensitive to their structure. The problem with this account is that there is no explanation as to why these two components must be compatible, other than by ad hoc assumption (convention) to exclude nonsystematic variants that, e.g., mix prefix and pos...

This paper outlines the initial stages in the acquisition of dislocations (as in (1)) by young francophones before the age of 2;6. Dislocations are shown to be derived by adjunction to IP or CP in the child language. A structure-building analysis of the data reveals that the ability of the child to implement CP is a prerequisite for certain types of dislocations. The implications of my results ...

The focus of this article is to develop computationally efficient mathematical morphology operators on hypergraphs. To this aim we consider lattice structures on hypergraphs on which we build morphological operators. We develop a pair of dual adjunctions between the vertex set and the hyper edge set of a hypergraph H , by defining a vertex-hyperedge correspondence. This allows us to recover the...