We introduce novel mathematical models and algorithms to generate (shortest or k different) explanations for biomedical queries, using answer set programming. We implement these algorithms and integrate them in BIOQUERY-ASP. We illustrate the usefulness of these methods with some complex biomedical queries related to drug discovery, over the biomedical knowledge resources PHARMGKB, DRUGBANK, BIOGRID, CTD, SIDER, DISEASE ONTOLOGY and ORPHADATA. To appear in Theory and Practice of Logic Programming (TPLP).

HOL(y)Hammer is an online AI/ATP service for formal (computer-understandable) mathematics encoded in the HOL Light system. The service allows its users to upload and automatically process an arbitrary formal development (project) based on HOL Light, and to attack arbitrary conjectures that use the concepts defined in some of the uploaded projects. For that, the service uses several automated reasoning systems combined with several premise selection methods trained on all the project proofs. The projects that are readily available on the server for such query answering include the recent versions of the Flyspeck, Multivariate Analysis and Complex Analysis libraries. The service runs on a 48-CPU server, currently employing in parallel for each task 7 AI/ATP combinations and 4 decision procedures that contribute to its overall performance. The system is also available for local installation by interested users, who can customize it for their own proof development. An Emacs interface allowing parallel asynchronous queries to the service is also provided. The overall structure of the service is outlined, problems that arise and their solutions are discussed, and an initial account of using the system is given.

Learning probabilistic logic programming languages is receiving an increasing attention and systems are available for learning the parameters (PRISM, LeProbLog, LFI-ProbLog and EMBLEM) or both the structure and the parameters (SEM-CP-logic and SLIPCASE) of these languages. In this paper we present the algorithm SLIPCOVER for "Structure LearnIng of Probabilistic logic programs by searChing OVER the clause space". It performs a beam search in the space of probabilistic clauses and a greedy search in the space of theories, using the log likelihood of the data as the guiding heuristics. To estimate the log likelihood SLIPCOVER performs Expectation Maximization with EMBLEM. The algorithm has been tested on five real world datasets and compared with SLIPCASE, SEM-CP-logic, Aleph and two algorithms for learning Markov Logic Networks (Learning using Structural Motifs (LSM) and ALEPH++ExactL1). SLIPCOVER achieves higher areas under the precision-recall and ROC curves in most cases.

This paper presents a new application of logic programming to a real-life problem in hydraulic engineering. The work is developed as a collaboration of computer scientists and hydraulic engineers, and applies Constraint Logic Programming to solve a hard combinatorial problem. This application deals with one aspect of the design of a water distribution network, i.e., the valve isolation system design. We take the formulation of the problem by [Giustolisi and Savic, 2008] and show how, thanks to constraint propagation, we can get better solutions than the best solution known in the literature for the Apulian distribution network.

Since it is a relatively new concept, little is known about the computational complexity of fuzzy answer set programming (FASP) and almost no techniques are available to compute answer sets of FASP programs. Furthermore, the connections of FASP to other paradigms of nonmonotonic reasoning with continuous values are largely unexplored. In our disertation, we contribute to the ongoing research on FASP on two different levels: complexity and connections to fuzzy modal logics.

We investigate the  complexity of  satisfiability for one-agent refinement modal logic (RML), an extension of basic modal logic (ML) obtained by adding refinement quantifiers on structures.  RML is known to have the same expressiveness as ML, but the translation of RML into ML is of non-elementary complexity, and RML is at least doubly exponentially more succinct than ML. In this paper we show that RML-satisfiability is `only' singly exponentially harder than ML-satisfiability, the latter being a well-known PSPACE-complete problem.

Probabilistic logics combine the expressive power of logic with the ability to reason with uncertainty. Several probabilistic logic languages have been proposed in the past, each of them with their own features. In this paper, we propose a new probabilistic constraint logic programming language, which combines constraint logic programming with probabilistic reasoning. The language supports modeling of discrete as well as continuous probability distributions by expressing constraints on random variables. We introduce the declarative semantics of this language, present an exact inference algorithm to derive bounds on the joint probability distributions consistent with the specified constraints, and give experimental results. The results obtained are encouraging, indicating that inference in our language is feasible for solving challenging problems.

In recent years Predicate Invention has been under-explored within Inductive Logic Programming due to difficulties in formulating efficient search mechanisms. However, a recent paper demonstrated that both predicate invention and the learning of recursion can be efficiently implemented for regular and context-free grammars, by way of abduction with respect to a meta-interpreter. New predicate symbols are introduced as constants representing existentially quantified higher-order variables. In this paper we generalise the approach of Meta-Interpretive Learning (MIL) to that of learning higher-order dyadic datalog programs. We show that with an infinite signature the higher-order dyadic datalog class H 2 2 has universal Turing expressivity though H 2 2 is decidable given a finite signature. Additionally we show that Knuth-Bendix ordering of the hypothesis space together with logarithmic clause bounding allows our Dyadic MIL implementation Metagol D to PAC-learn minimal cardinailty H 2 2 definitions. This result is consistent with our experiments which indicate that Metagol D efficiently learns compact H 2 2 definitions involving predicate invention for robotic strategies and higher-order concepts in the NELL language learning domain.

In this paper, the fixed point semantics developed in [Lobo et al., 1992] is generalized to disjunctive logic programs with default negation and over arbitrary structures, and proved to coincide with the stable model semantics. By using the tool of ultraproducts, a preservation theorem, which asserts that a disjunctive logic program without default negation is bounded with respect to the proposed semantics if and only if it has a first-order equivalent, is then obtained. For the disjunctive logic programs with default negation, a sufficient condition assuring the first-order expressibility is also proposed.

Projection in the situation calculus refers to answering queries about the future evolutions of the modeled domain, while progression refers to updating the logical representation of the initial state so that it reflects the changes due to an executed action. In the general case projection is not decidable and progression may require second-order logic. In this paper we focus on a recent result about the decidability of projection and use it to drive results for the problem of progression. In particular we contribute with the following: (i) a major result showing that for a large class of intuitive action theories with bounded unknowns a first-order progression always exists and can be computed; (ii) a comprehensive classification of the known classes that can be progressed in first-order; (iii) a novel account of nondeterministic actions in the situation calculus.