The Functional Perspective on Advanced Logic Programming

The basics of logic programming, as embodied by Prolog, are generally well-known in the programming language community. However, more advanced techniques, such as tabling, answer subsumption and probabilistic logic programming fail to attract the attention of a larger audience. The cause for the community\u27s seemingly limited interest lies with the presentation of these features: the literature frequently focuses on implementations and examples that do little to aid the understanding of non-experts in the field. The key point is that many of these advanced logic programming features can be characterised in more generally known, more accessible terms. In my research I try to reconcile these advanced concepts from logic programming (Tabling, Answer subsumption and probabilistic programming) with concepts from functional programming (effects, monads and applicative functors)

Declarative programming for agent applications

This paper introduces the execution model of a declarative programming language intended for agent applications. Features supported by the language include functional and logic programming idioms, higher-order functions, modal computation, probabilistic computation, and some theorem-proving capabilities. The need for these features is motivated and examples are given to illustrate the central ideas

Computable de Finetti measures

We prove a computable version of de Finetti's theorem on exchangeable sequences of real random variables. As a consequence, exchangeable stochastic processes expressed in probabilistic functional programming languages can be automatically rewritten as procedures that do not modify non-local state. Along the way, we prove that a distribution on the unit interval is computable if and only if its moments are uniformly computable.Comment: 32 pages. Final journal version; expanded somewhat, with minor corrections. To appear in Annals of Pure and Applied Logic. Extended abstract appeared in Proceedings of CiE '09, LNCS 5635, pp. 218-23

Explanations as Programs in Probabilistic Logic Programming

The generation of comprehensible explanations is an essential feature of modern artificial intelligence systems. In this work, we consider probabilistic logic programming, an extension of logic programming which can be useful to model domains with relational structure and uncertainty. Essentially, a program specifies a probability distribution over possible worlds (i.e., sets of facts). The notion of explanation is typically associated with that of a world, so that one often looks for the most probable world as well as for the worlds where the query is true. Unfortunately, such explanations exhibit no causal structure. In particular, the chain of inferences required for a specific prediction (represented by a query) is not shown. In this paper, we propose a novel approach where explanations are represented as programs that are generated from a given query by a number of unfolding-like transformations. Here, the chain of inferences that proves a given query is made explicit. Furthermore, the generated explanations are minimal (i.e., contain no irrelevant information) and can be parameterized w.r.t. a specification of visible predicates, so that the user may hide uninteresting details from explanations.Comment: Published as: Vidal, G. (2022). Explanations as Programs in Probabilistic Logic Programming. In: Hanus, M., Igarashi, A. (eds) Functional and Logic Programming. FLOPS 2022. Lecture Notes in Computer Science, vol 13215. Springer, Cham. The final authenticated publication is available online at https://doi.org/10.1007/978-3-030-99461-7_1