The PITA System: Tabling and Answer Subsumption for Reasoning under Uncertainty

Many real world domains require the representation of a measure of uncertainty. The most common such representation is probability, and the combination of probability with logic programs has given rise to the field of Probabilistic Logic Programming (PLP), leading to languages such as the Independent Choice Logic, Logic Programs with Annotated Disjunctions (LPADs), Problog, PRISM and others. These languages share a similar distribution semantics, and methods have been devised to translate programs between these languages. The complexity of computing the probability of queries to these general PLP programs is very high due to the need to combine the probabilities of explanations that may not be exclusive. As one alternative, the PRISM system reduces the complexity of query answering by restricting the form of programs it can evaluate. As an entirely different alternative, Possibilistic Logic Programs adopt a simpler metric of uncertainty than probability. Each of these approaches -- general PLP, restricted PLP, and Possibilistic Logic Programming -- can be useful in different domains depending on the form of uncertainty to be represented, on the form of programs needed to model problems, and on the scale of the problems to be solved. In this paper, we show how the PITA system, which originally supported the general PLP language of LPADs, can also efficiently support restricted PLP and Possibilistic Logic Programs. PITA relies on tabling with answer subsumption and consists of a transformation along with an API for library functions that interface with answer subsumption

Actual Causation in CP-logic

Given a causal model of some domain and a particular story that has taken place in this domain, the problem of actual causation is deciding which of the possible causes for some effect actually caused it. One of the most influential approaches to this problem has been developed by Halpern and Pearl in the context of structural models. In this paper, I argue that this is actually not the best setting for studying this problem. As an alternative, I offer the probabilistic logic programming language of CP-logic. Unlike structural models, CP-logic incorporates the deviant/default distinction that is generally considered an important aspect of actual causation, and it has an explicitly dynamic semantics, which helps to formalize the stories that serve as input to an actual causation problem

Tabling and Answer Subsumption for Reasoning on Logic Programs with Annotated Disjunctions

Abstract Probabilistic Logic Programming is an active field of research, with many proposals for languages, semantics and reasoning algorithms. One such proposal, Logic Programming with Annotated Disjunctions (LPADs) represents probabilistic information in a sound and simple way. This paper presents the algorithm "Probabilistic Inference with Tabling and Answer subsumption" (PITA) for computing the probability of queries. Answer subsumption is a feature of tabling that allows the combination of different answers for the same subgoal in the case in which a partial order can be defined over them. We have applied it in our case since probabilistic explanations (stored as BDDs in PITA) possess a natural lattice structure. PITA has been implemented in XSB and compared with ProbLog, cplint and CVE. The results show that, in almost all cases, PITA is able to solve larger problems and is faster than competing algorithms

Monitoring Complex Processes to Verify System Conformance: A Declarative Rule-Based Framework

Over the last 60 years, computers and software have favoured incredible advancements in every field. Nowadays, however, these systems are so complicated that it is difficult – if not challenging – to understand whether they meet some requirement or are able to show some desired behaviour or property. This dissertation introduces a Just-In-Time (JIT) a posteriori approach to perform the conformance check to identify any deviation from the desired behaviour as soon as possible, and possibly apply some corrections. The declarative framework that implements our approach – entirely developed on the promising open source forward-chaining Production Rule System (PRS) named Drools – consists of three components: 1. a monitoring module based on a novel, efficient implementation of Event Calculus (EC), 2. a general purpose hybrid reasoning module (the first of its genre) merging temporal, semantic, fuzzy and rule-based reasoning, 3. a logic formalism based on the concept of expectations introducing Event-Condition-Expectation rules (ECE-rules) to assess the global conformance of a system. The framework is also accompanied by an optional module that provides Probabilistic Inductive Logic Programming (PILP). By shifting the conformance check from after execution to just in time, this approach combines the advantages of many a posteriori and a priori methods proposed in literature. Quite remarkably, if the corrective actions are explicitly given, the reactive nature of this methodology allows to reconcile any deviations from the desired behaviour as soon as it is detected. In conclusion, the proposed methodology brings some advancements to solve the problem of the conformance checking, helping to fill the gap between humans and the increasingly complex technology.Negli ultimi 60 anni, i computer e i programmi hanno favorito incredibili avanzamenti in ogni campo. Oggigiorno, purtroppo, questi sistemi sono così complicati che è difficile – se non impossibile – capire se soddisfano qualche requisito o mostrano un comportamento o una proprietà desiderati. Questa tesi introduce un approccio a posteriori Just-In-Time (JIT) per effettuare il controllo di conformità ed identificare appena possibile ogni deviazione dal comportamento desiderato, ed eventualmente applicare qualche correzione. Il framework dichiarativo che implementa il nostro approccio – interamente sviluppato su una promettente piattaforma open source di Production Rule System (PRS) chiamata Drools – si compone di tre elementi: 1. un modulo per il monitoraggio basato su una nuova implementazione efficiente di Event Calculus (EC), 2. un modulo generale per il ragionamento ibrido (il primo del suo genere) che supporta ragionamento temporale, semantico, fuzzy e a regole, 3. un formalismo logico basato sul concetto di aspettativa che introduce le Event-Condition-Expectation rules (ECE-rules) per valutare la conformità globale di un sistema. Il framework è anche accompagnato da un modulo opzionale che fornisce Probabilistic Inductive Logic Programming (PILP). Spostando il controllo di conformità da dopo l’esecuzione ad appena in tempo, questo approccio combina i vantaggi di molti metodi a posteriori e a priori proposti in letteratura. Si noti che, se le azioni correttive sono fornite esplicitamente, la natura reattiva di questo metodo consente di conciliare le deviazioni dal comportamento desiderato non appena questo viene rilevato. In conclusione, la metodologia proposta introduce alcuni avanzamenti per risolvere il problema del controllo di conformità, contribuendo a colmare il divario tra l’uomo e la tecnologia, sempre più complessa

Inference with logic programs with annotated disjunctions under the well founded semantics

Logic Programs with Annotated Disjunctions (LPADs) allow to express probabilistic information in logic programming. The semantics of an LPAD is given in terms of well founded models of the normal logic programs obtained by selecting one disjunct from each ground LPAD clause. The paper presents SLGAD resolution that computes the (conditional) probability of a ground query from an LPAD and is based on SLG resolution for normal logic programs. SLGAD is evaluated on classical benchmarks for well founded semantics inference algorithms, namely the stalemate game and the ancestor relation. SLGAD is compared with Cilog2 and SLDNFAD, an algorithm based on SLDNF, on the programs that are modularly acyclic. The results show that SLGAD deals correctly with cyclic programs and, even if it is more expensive than SLDNFAD on problems where SLDNFAD succeeds, is faster than Cilog2 when the query is true in an exponential number of instances

SLGAD Resolution for Inference on Logic Programs with Annotated Disjunctions

Logic Programs with Annotated Disjunctions (LPADs) allow to express probabilistic information in logic programming. The semantics of an LPAD is given in terms of well-founded models of the normal logic programs obtained by selecting one disjunct from each ground LPAD clause. Inference on LPADs can be performed using either the system Ailog2, that was developed for the Independent Choice Logic, or SLDNFAD, an algorithm based on SLDNF. However, both of these algorithms run the risk of going into infinite loops and of performing redundant computations. In order to avoid these problems, we present SLGAD resolution that computes the (conditional) probability of a ground query from a range-restricted LPAD and is based on SLG resolution for normal logic programs. As SLG, it uses tabling to avoid some infinite loops and to avoid redundant computations. The performances of SLGAD are evaluated on classical benchmarks for normal logic programs under the well-founded semantics, namely a 2-person game and the ancestor relation, and on a game of dice. SLGAD is compared with Ailog2 and SLDNFAD on the problems in which they do not go into infinite loops, namely those that are described by a modularly acyclic program. On the 2-person game and the ancestor relation, SLGAD is more expensive than SLDNFAD on problems where SLDNFAD succeeds but is faster than Ailog2 when the query is true in an exponential number of instances. If the program requires the repeated computation of similar goals, as for the dice game, then SLGAD outperforms both Ailog2 and SLDNFAD