126,430 research outputs found
Spatial Logics for Bigraphs
Bigraphs are emerging as an interesting model for concurrent calculi, like CCS, pi-calculus, and Petri nets. Bigraphs are built orthogonally on two structures: a hierarchical place graph for locations and a link (hyper-)graph for connections. With the aim of describing bigraphical structures, we introduce a general framework for logics whose terms represent arrows in monoidal categories. We then instantiate the framework to bigraphical structures and obtain a logic that is a natural composition of a place graph logic and a link graph logic. We explore the concepts of separation and sharing in these logics and we prove that they generalise some known spatial logics for trees, graphs and tree contexts
Lewis meets Brouwer: constructive strict implication
C. I. Lewis invented modern modal logic as a theory of "strict implication".
Over the classical propositional calculus one can as well work with the unary
box connective. Intuitionistically, however, the strict implication has greater
expressive power than the box and allows to make distinctions invisible in the
ordinary syntax. In particular, the logic determined by the most popular
semantics of intuitionistic K becomes a proper extension of the minimal normal
logic of the binary connective. Even an extension of this minimal logic with
the "strength" axiom, classically near-trivial, preserves the distinction
between the binary and the unary setting. In fact, this distinction and the
strong constructive strict implication itself has been also discovered by the
functional programming community in their study of "arrows" as contrasted with
"idioms". Our particular focus is on arithmetical interpretations of the
intuitionistic strict implication in terms of preservativity in extensions of
Heyting's Arithmetic.Comment: Our invited contribution to the collection "L.E.J. Brouwer, 50 years
later
Coherence of Proof-Net Categories
The notion of proof-net category defined in this paper is closely related to
graphs implicit in proof nets for the multiplicative fragment without constant
propositions of linear logic. Analogous graphs occur in Kelly's and Mac Lane's
coherence theorem for symmetric monoidal closed categories. A coherence theorem
with respect to these graphs is proved for proof-net categories. Such a
coherence theorem is also proved in the presence of arrows corresponding to the
mix principle of linear logic. The notion of proof-net category catches the
unit free fragment of the notion of star-autonomous category, a special kind of
symmetric monoidal closed category.Comment: 40 pages, 1 figur
Optimising visual solutions for complex strategic scenarios : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Psychology at Massey University, Wellington, New Zealand
Attempts to pre-emptively improve post-disaster outcomes need to reflect an improved understanding of cognitive adaptations made by collaborating researchers and practitioners. This research explored the use of visual logic models to enhance the quality of decisions being made by these professionals. The research looked at the way visual representations serve to enhance these decisions, as part of cognitive adaptations to considering the complexity of relevant pre-disaster conditions constituting community resilience. It was proposed that a visual logic model display, using boxes and arrows to display linkages between activities and downstream objectives, could support effective, efficient and responsive approaches to relevant community resilience interventions being carried out in a pre-disaster context.
The first of three phases comprising this thesis used Q-methodology to identify patterns of opinions concerning building a shared framework of pre-disaster, community resilience indicators for this purpose. Three patterns identified helped to assess the needs for applied research undertaken in phase two. The second phase of this thesis entailed building an action-focused logic model to enhance associated collaborations between emergency management practitioners and researchers. An analysis of participant interviews determined that the process used to build this logic model served as a catalyst for research which could help improve community resilience interventions. The third phase used an experimental approach to different display formats produced during phase two to test whether a visual logic model display stimulated a higher quality of decisions, compared with a more conventional, text-based chart of key performance indicators. Results supported the use of similar methods for much larger scale research to assess how information displays support emergency management decisions with wide-ranging, longer-term implications.
Overall, results from these three phases indicate that certain logic model formats can help foster collaborative efforts to improve characteristics of community resilience against disasters. This appears to occur when a logic model forms an integrated component of efficient cognitive dynamics across a network of decision making agents. This understanding of logic model function highlights clear opportunities for further research. It also represents a novel contribution to knowledge about using logic models to support emergency management decisions with complex, long term implications
Synthesizing Functional Reactive Programs
Functional Reactive Programming (FRP) is a paradigm that has simplified the
construction of reactive programs. There are many libraries that implement
incarnations of FRP, using abstractions such as Applicative, Monads, and
Arrows. However, finding a good control flow, that correctly manages state and
switches behaviors at the right times, still poses a major challenge to
developers. An attractive alternative is specifying the behavior instead of
programming it, as made possible by the recently developed logic: Temporal
Stream Logic (TSL). However, it has not been explored so far how Control Flow
Models (CFMs), as synthesized from TSL specifications, can be turned into
executable code that is compatible with libraries building on FRP. We bridge
this gap, by showing that CFMs are indeed a suitable formalism to be turned
into Applicative, Monadic, and Arrowized FRP. We demonstrate the effectiveness
of our translations on a real-world kitchen timer application, which we
translate to a desktop application using the Arrowized FRP library Yampa, a web
application using the Monadic threepenny-gui library, and to hardware using the
Applicative hardware description language ClaSH.Comment: arXiv admin note: text overlap with arXiv:1712.0024
The Isbell monad
In 1966, John Isbell introduced a construction on categories which he termed
the "couple category" but which has since come to be known as the Isbell
envelope. The Isbell envelope, which combines the ideas of contravariant and
covariant presheaves, has found applications in category theory, logic, and
differential geometry. We clarify its meaning by exhibiting the assignation
sending a locally small category to its Isbell envelope as the action on
objects of a pseudomonad on the 2-category of locally small categories; this is
the Isbell monad of the title. We characterise the pseudoalgebras of the Isbell
monad as categories equipped with a cylinder factorisation system; this notion,
which appears to be new, is an extension of Freyd and Kelly's notion of
factorisation system from orthogonal classes of arrows to orthogonal classes of
cocones and cones.Comment: 21 page
A Bunched Logic for Conditional Independence
Independence and conditional independence are fundamental concepts for reasoning about groups of random variables in probabilistic programs. Verification methods for independence are still nascent, and existing methods cannot handle conditional independence. We extend the logic of bunched implications (BI) with a non-commutative conjunction and provide a model based on Markov kernels; conditional independence can be directly captured as a logical formula in this model. Noting that Markov kernels are Kleisli arrows for the distribution monad, we then introduce a second model based on the powerset monad and show how it can capture join dependency, a non-probabilistic analogue of conditional independence from database theory. Finally, we develop a program logic for verifying conditional independence in probabilistic programs
Classical Structures Based on Unitaries
Starting from the observation that distinct notions of copying have arisen in
different categorical fields (logic and computation, contrasted with quantum
mechanics) this paper addresses the question of when, or whether, they may
coincide. Provided all definitions are strict in the categorical sense, we show
that this can never be the case. However, allowing for the defining axioms to
be taken up to canonical isomorphism, a close connection between the classical
structures of categorical quantum mechanics, and the categorical property of
self-similarity familiar from logical and computational models becomes
apparent.
The required canonical isomorphisms are non-trivial, and mix both typed
(multi-object) and untyped (single-object) tensors and structural isomorphisms;
we give coherence results that justify this approach.
We then give a class of examples where distinct self-similar structures at an
object determine distinct matrix representations of arrows, in the same way as
classical structures determine matrix representations in Hilbert space. We also
give analogues of familiar notions from linear algebra in this setting such as
changes of basis, and diagonalisation.Comment: 24 pages,7 diagram
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