Probabilistic Programming Concepts

A multitude of different probabilistic programming languages exists today, all extending a traditional programming language with primitives to support modeling of complex, structured probability distributions. Each of these languages employs its own probabilistic primitives, and comes with a particular syntax, semantics and inference procedure. This makes it hard to understand the underlying programming concepts and appreciate the differences between the different languages. To obtain a better understanding of probabilistic programming, we identify a number of core programming concepts underlying the primitives used by various probabilistic languages, discuss the execution mechanisms that they require and use these to position state-of-the-art probabilistic languages and their implementation. While doing so, we focus on probabilistic extensions of logic programming languages such as Prolog, which have been developed since more than 20 years

Using SWISH to realise interactive web based tutorials for logic based languages

Programming environments have evolved from purely text based to using graphical user interfaces, and now we see a move towards web based interfaces, such as Jupyter. Web based interfaces allow for the creation of interactive documents that consist of text and programs, as well as their output. The output can be rendered using web technology as, e.g., text, tables, charts or graphs. This approach is particularly suitable for capturing data analysis workflows and creating interactive educational material. This article describes SWISH, a web front-end for Prolog that consists of a web server implemented in SWI-Prolog and a client web application written in JavaScript. SWISH provides a web server where multiple users can manipulate and run the same material, and it can be adapted to support Prolog extensions. In this paper we describe the architecture of SWISH, and describe two case studies of extensions of Prolog, namely Probabilistic Logic Programming (PLP) and Logic Production System (LPS), which have used SWISH to provide tutorial sites

Probabilistic logic programming in 2P-KT

The work introduces an elastic and platform-agnostic approach to probabilistic logic programming aimed at linking this paradigm with modern mainstream programming platforms, thus widening its usability and portability (e.g. towards the JVM, Android, Python, and JavaScript platforms). We design our solution as an extension of the 2P-Kt symbolic AI ecosystem to inherit its multi-platform and multi-paradigm nature

Logic-Based Decision Support for Strategic Environmental Assessment

Strategic Environmental Assessment is a procedure aimed at introducing systematic assessment of the environmental effects of plans and programs. This procedure is based on the so-called coaxial matrices that define dependencies between plan activities (infrastructures, plants, resource extractions, buildings, etc.) and positive and negative environmental impacts, and dependencies between these impacts and environmental receptors. Up to now, this procedure is manually implemented by environmental experts for checking the environmental effects of a given plan or program, but it is never applied during the plan/program construction. A decision support system, based on a clear logic semantics, would be an invaluable tool not only in assessing a single, already defined plan, but also during the planning process in order to produce an optimized, environmentally assessed plan and to study possible alternative scenarios. We propose two logic-based approaches to the problem, one based on Constraint Logic Programming and one on Probabilistic Logic Programming that could be, in the future, conveniently merged to exploit the advantages of both. We test the proposed approaches on a real energy plan and we discuss their limitations and advantages.Comment: 17 pages, 1 figure, 26th Int'l. Conference on Logic Programming (ICLP'10

Probabilistic (logic) programming concepts

A multitude of different probabilistic programming languages exists today, all extending a traditional programming language with primitives to support modeling of complex, structured probability distributions. Each of these languages employs its own probabilistic primitives, and comes with a particular syntax, semantics and inference procedure. This makes it hard to understand the underlying programming concepts and appreciate the differences between the different languages. To obtain a better understanding of probabilistic programming, we identify a number of core programming concepts underlying the primitives used by various probabilistic languages, discuss the execution mechanisms that they require and use these to position and survey state-of-the-art probabilistic languages and their implementation. While doing so, we focus on probabilistic extensions of logic programming languages such as Prolog, which have been considered for over 20 years

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

Integration of Logic and Probability in Terminological and Inductive Reasoning

This thesis deals with Statistical Relational Learning (SRL), a research area combining principles and ideas from three important subfields of Artificial Intelligence: machine learn- ing, knowledge representation and reasoning on uncertainty. Machine learning is the study of systems that improve their behavior over time with experience; the learning process typi- cally involves a search through various generalizations of the examples, in order to discover regularities or classification rules. A wide variety of machine learning techniques have been developed in the past fifty years, most of which used propositional logic as a (limited) represen- tation language. Recently, more expressive knowledge representations have been considered, to cope with a variable number of entities as well as the relationships that hold amongst them. These representations are mostly based on logic that, however, has limitations when reason- ing on uncertain domains. These limitations have been lifted allowing a multitude of different formalisms combining probabilistic reasoning with logics, databases or logic programming, where probability theory provides a formal basis for reasoning on uncertainty. In this thesis we consider in particular the proposals for integrating probability in Logic Programming, since the resulting probabilistic logic programming languages present very in- teresting computational properties. In Probabilistic Logic Programming, the so-called "dis- tribution semantics" has gained a wide popularity. This semantics was introduced for the PRISM language (1995) but is shared by many other languages: Independent Choice Logic, Stochastic Logic Programs, CP-logic, ProbLog and Logic Programs with Annotated Disjunc- tions (LPADs). A program in one of these languages defines a probability distribution over normal logic programs called worlds. This distribution is then extended to queries and the probability of a query is obtained by marginalizing the joint distribution of the query and the programs. The languages following the distribution semantics differ in the way they define the distribution over logic programs. The first part of this dissertation presents techniques for learning probabilistic logic pro- grams under the distribution semantics. Two problems are considered: parameter learning and structure learning, that is, the problems of inferring values for the parameters or both the structure and the parameters of the program from data. This work contributes an algorithm for parameter learning, EMBLEM, and two algorithms for structure learning (SLIPCASE and SLIPCOVER) of probabilistic logic programs (in particular LPADs). EMBLEM is based on the Expectation Maximization approach and computes the expectations directly on the Binary De- cision Diagrams that are built for inference. SLIPCASE performs a beam search in the space of LPADs while SLIPCOVER performs a beam search in the space of probabilistic clauses and a greedy search in the space of LPADs, improving SLIPCASE performance. All learning approaches have been evaluated in several relational real-world domains. The second part of the thesis concerns the field of Probabilistic Description Logics, where we consider a logical framework suitable for the Semantic Web. Description Logics (DL) are a family of formalisms for representing knowledge. Research in the field of knowledge repre- sentation and reasoning is usually focused on methods for providing high-level descriptions of the world that can be effectively used to build intelligent applications. Description Logics have been especially effective as the representation language for for- mal ontologies. Ontologies model a domain with the definition of concepts and their properties and relations. Ontologies are the structural frameworks for organizing information and are used in artificial intelligence, the Semantic Web, systems engineering, software engineering, biomedical informatics, etc. They should also allow to ask questions about the concepts and in- stances described, through inference procedures. Recently, the issue of representing uncertain information in these domains has led to probabilistic extensions of DLs. The contribution of this dissertation is twofold: (1) a new semantics for the Description Logic SHOIN(D) , based on the distribution semantics for probabilistic logic programs, which embeds probability; (2) a probabilistic reasoner for computing the probability of queries from uncertain knowledge bases following this semantics. The explanations of queries are encoded in Binary Decision Diagrams, with the same technique employed in the learning systems de- veloped for LPADs. This approach has been evaluated on a real-world probabilistic ontology

On the role of Computational Logic in Data Science: representing, learning, reasoning, and explaining knowledge

In this thesis we discuss in what ways computational logic (CL) and data science (DS) can jointly contribute to the management of knowledge within the scope of modern and future artificial intelligence (AI), and how technically-sound software technologies can be realised along the path. An agent-oriented mindset permeates the whole discussion, by stressing pivotal role of autonomous agents in exploiting both means to reach higher degrees of intelligence. Accordingly, the goals of this thesis are manifold. First, we elicit the analogies and differences among CL and DS, hence looking for possible synergies and complementarities along 4 major knowledge-related dimensions, namely representation, acquisition (a.k.a. learning), inference (a.k.a. reasoning), and explanation. In this regard, we propose a conceptual framework through which bridges these disciplines can be described and designed. We then survey the current state of the art of AI technologies, w.r.t. their capability to support bridging CL and DS in practice. After detecting lacks and opportunities, we propose the notion of logic ecosystem as the new conceptual, architectural, and technological solution supporting the incremental integration of symbolic and sub-symbolic AI. Finally, we discuss how our notion of logic ecosys- tem can be reified into actual software technology and extended towards many DS-related directions

Causal inference in cplint

cplint is a suite of programs for reasoning and learning with Probabilistic Logic Programming languages that follow the distribution semantics. In this paper we describe how we have extended cplint to perform causal reasoning. In particular, we consider Pearl's do calculus for models where all the variables are measured. The two cplint modules for inference, PITA and MCINTYRE, have been extended for computing the effect of actions/interventions on these models. We also executed experiments comparing exact and approximate inference with conditional and causal queries, showing that causal inference is often cheaper than conditional inference