5,257 research outputs found
A framework for protein and membrane interactions
We introduce the BioBeta Framework, a meta-model for both protein-level and
membrane-level interactions of living cells. This formalism aims to provide a
formal setting where to encode, compare and merge models at different
abstraction levels; in particular, higher-level (e.g. membrane) activities can
be given a formal biological justification in terms of low-level (i.e.,
protein) interactions. A BioBeta specification provides a protein signature
together a set of protein reactions, in the spirit of the kappa-calculus.
Moreover, the specification describes when a protein configuration triggers one
of the only two membrane interaction allowed, that is "pinch" and "fuse". In
this paper we define the syntax and semantics of BioBeta, analyse its
properties, give it an interpretation as biobigraphical reactive systems, and
discuss its expressivity by comparing with kappa-calculus and modelling
significant examples. Notably, BioBeta has been designed after a bigraphical
metamodel for the same purposes. Hence, each instance of the calculus
corresponds to a bigraphical reactive system, and vice versa (almost).
Therefore, we can inherith the rich theory of bigraphs, such as the automatic
construction of labelled transition systems and behavioural congruences
A coalgebraic semantics for causality in Petri nets
In this paper we revisit some pioneering efforts to equip Petri nets with
compact operational models for expressing causality. The models we propose have
a bisimilarity relation and a minimal representative for each equivalence
class, and they can be fully explained as coalgebras on a presheaf category on
an index category of partial orders. First, we provide a set-theoretic model in
the form of a a causal case graph, that is a labeled transition system where
states and transitions represent markings and firings of the net, respectively,
and are equipped with causal information. Most importantly, each state has a
poset representing causal dependencies among past events. Our first result
shows the correspondence with behavior structure semantics as proposed by
Trakhtenbrot and Rabinovich. Causal case graphs may be infinitely-branching and
have infinitely many states, but we show how they can be refined to get an
equivalent finitely-branching model. In it, states are equipped with
symmetries, which are essential for the existence of a minimal, often
finite-state, model. The next step is constructing a coalgebraic model. We
exploit the fact that events can be represented as names, and event generation
as name generation. Thus we can apply the Fiore-Turi framework: we model causal
relations as a suitable category of posets with action labels, and generation
of new events with causal dependencies as an endofunctor on this category. Then
we define a well-behaved category of coalgebras. Our coalgebraic model is still
infinite-state, but we exploit the equivalence between coalgebras over a class
of presheaves and History Dependent automata to derive a compact
representation, which is equivalent to our set-theoretical compact model.
Remarkably, state reduction is automatically performed along the equivalence.Comment: Accepted by Journal of Logical and Algebraic Methods in Programmin
Causality and the semantics of provenance
Provenance, or information about the sources, derivation, custody or history
of data, has been studied recently in a number of contexts, including
databases, scientific workflows and the Semantic Web. Many provenance
mechanisms have been developed, motivated by informal notions such as
influence, dependence, explanation and causality. However, there has been
little study of whether these mechanisms formally satisfy appropriate policies
or even how to formalize relevant motivating concepts such as causality. We
contend that mathematical models of these concepts are needed to justify and
compare provenance techniques. In this paper we review a theory of causality
based on structural models that has been developed in artificial intelligence,
and describe work in progress on a causal semantics for provenance graphs.Comment: Workshop submissio
On an Intuitionistic Logic for Pragmatics
We reconsider the pragmatic interpretation of intuitionistic logic [21]
regarded as a logic of assertions and their justications and its relations with classical
logic. We recall an extension of this approach to a logic dealing with assertions
and obligations, related by a notion of causal implication [14, 45]. We focus on
the extension to co-intuitionistic logic, seen as a logic of hypotheses [8, 9, 13] and on
polarized bi-intuitionistic logic as a logic of assertions and conjectures: looking at the
S4 modal translation, we give a denition of a system AHL of bi-intuitionistic logic
that correctly represents the duality between intuitionistic and co-intuitionistic logic,
correcting a mistake in previous work [7, 10]. A computational interpretation of cointuitionism
as a distributed calculus of coroutines is then used to give an operational
interpretation of subtraction.Work on linear co-intuitionism is then recalled, a linear
calculus of co-intuitionistic coroutines is dened and a probabilistic interpretation
of linear co-intuitionism is given as in [9]. Also we remark that by extending the
language of intuitionistic logic we can express the notion of expectation, an assertion
that in all situations the truth of p is possible and that in a logic of expectations
the law of double negation holds. Similarly, extending co-intuitionistic logic, we can
express the notion of conjecture that p, dened as a hypothesis that in some situation
the truth of p is epistemically necessary
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