No Arabic abstract
We consider multi-agent systems where agents actions and beliefs are determined aleatorically, or by the throw of dice. This system consists of possible worlds that assign distributions to independent random variables, and agents who assign probabilities to these possible worlds. We present a novel syntax and semantics for such system, and show that they generalise Modal Logic. We also give a sound and complete calculus for reasoning in the base semantics, and a sound calculus for the full modal semantics, that we conjecture to be complete. Finally we discuss some application to reasoning about game playing agents.
In this paper, we show how to interpret a language featuring concurrency, references and replication into proof nets, which correspond to a fragment of differential linear logic. We prove a simulation and adequacy theorem. A key element in our translation are routing areas, a family of nets used to implement communication primitives which we define and study in detail.
In probabilistic coherence spaces, a denotational model of probabilistic functional languages, morphisms are analytic and therefore smooth. We explore two related applications of the corresponding derivatives. First we show how derivatives allow to compute the expectation of execution time in the weak head reduction of probabilistic PCF (pPCF). Next we apply a general notion of local differential of morphisms to the proof of a Lipschitz property of these morphisms allowing in turn to relate the observational distance on pPCF terms to a distance the model is naturally equipped with. This suggests that extending probabilistic programming languages with derivatives, in the spirit of the differential lambda-calculus, could be quite meaningful.
This paper studies the quantitative refinements of Abramskys applicative similarity and bisimilarity in the context of a generalisation of Fuzz, a call-by-value $lambda$-calculus with a linear type system that can express programs sensitivity, enriched with algebraic operations emph{`a la} Plotkin and Power. To do so a general, abstract framework for studying behavioural relations taking values over quantales is defined according to Lawveres analysis of generalised metric spaces. Barrs notion of relator (or lax extension) is then extended to quantale-valued relations adapting and extending results from the field of monoidal topology. Abstract notions of quantale-valued effectful applicative similarity and bisimilarity are then defined and proved to be a compatible generalised metric (in the sense of Lawvere) and pseudometric, respectively, under mild conditions.
The Shapes Constraint Language (SHACL) allows for formalizing constraints over RDF data graphs. A shape groups a set of constraints that may be fulfilled by nodes in the RDF graph. We investigate the problem of containment between SHACL shapes. One shape is contained in a second shape if every graph node meeting the constraints of the first shape also meets the constraints of the second. To decide shape containment, we map SHACL shape graphs into description logic axioms such that shape containment can be answered by description logic reasoning. We identify several, increasingly tight syntactic restrictions of SHACL for which this approach becomes sound and complete.
In a paper entitled Binary lambda calculus and combinatory logic, John Tromp presents a simple way of encoding lambda calculus terms as binary sequences. In what follows, we study the numbers of binary strings of a given size that represent lambda terms and derive results from their generating functions, especially that the number of terms of size n grows roughly like 1.963447954. .. n. In a second part we use this approach to generate random lambda terms using Boltzmann samplers.