scholarly journals The distribution semantics for normal programs with function symbols

2016 ◽  
Vol 77 ◽  
pp. 1-19 ◽  
Author(s):  
Fabrizio Riguzzi
Keyword(s):  
Distribution Semantics

scholarly journals The PITA system: Tabling and answer subsumption for reasoning under uncertainty

2011 ◽  
Vol 11 (4-5) ◽  
pp. 433-449 ◽  
Author(s):  
FABRIZIO RIGUZZI ◽  
TERRANCE SWIFT
Keyword(s):  
Logic Programming ◽  
Probabilistic Logic ◽  
Similar Distribution ◽  
Logic Programs ◽  
Reasoning Under Uncertainty ◽  
Complex Queries ◽  
Possibilistic Logic ◽  
Distribution Semantics ◽  
Measure Of Uncertainty ◽  
Very High

AbstractMany 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. We show that, by adapting its transformation and library functions, PITA can be parameterized to PITA(IND, EXC) which supports the restricted PLP of PRISM, including optimizations that reduce non-discriminating arguments and the computation of Viterbi paths. Furthermore, we show PITA to be competitive with PRISM for complex queries to Hidden Markov Model examples, and sometimes much faster. We further show how PITA can be parameterized to PITA(COUNT) which computes the number of different explanations for a subgoal, and to PITA(POSS) which scalably implements Possibilistic Logic Programming. PITA is a supported package in version 3.3 of XSB.

scholarly journals Lifted Variable Elimination for Probabilistic Logic Programming

2014 ◽  
Vol 14 (4-5) ◽  
pp. 681-695 ◽  
Author(s):  
ELENA BELLODI ◽  
EVELINA LAMMA ◽  
FABRIZIO RIGUZZI ◽  
VITOR SANTOS COSTA ◽  
RICCARDO ZESE
Keyword(s):  
Logic Programming ◽  
Random Variables ◽  
Probabilistic Logic ◽  
Probabilistic Logic Programming ◽  
Lifted Inference ◽  
Logical Frameworks ◽  
Variable Elimination ◽  
Causal Independence ◽  
Order Variable ◽  
Distribution Semantics

AbstractLifted inference has been proposed for various probabilistic logical frameworks in order to compute the probability of queries in a time that depends on the size of the domains of the random variables rather than the number of instances. Even if various authors have underlined its importance for probabilistic logic programming (PLP), lifted inference has been applied up to now only to relational languages outside of logic programming. In this paper we adapt Generalized Counting First Order Variable Elimination (GC-FOVE) to the problem of computing the probability of queries to probabilistic logic programs under the distribution semantics. In particular, we extend the Prolog Factor Language (PFL) to include two new types of factors that are needed for representing ProbLog programs. These factors take into account the existing causal independence relationships among random variables and are managed by the extension to variable elimination proposed by Zhang and Poole for dealing with convergent variables and heterogeneous factors. Two new operators are added to GC-FOVE for treating heterogeneous factors. The resulting algorithm, called LP2for Lifted Probabilistic Logic Programming, has been implemented by modifying the PFL implementation of GC-FOVE and tested on three benchmarks for lifted inference. A comparison with PITA and ProbLog2 shows the potential of the approach.

scholarly journals CHR(PRISM)-based probabilistic logic learning

2010 ◽  
Vol 10 (4-6) ◽  
pp. 433-447 ◽  
Author(s):  
JON SNEYERS ◽  
WANNES MEERT ◽  
JOOST VENNEKENS ◽  
YOSHITAKA KAMEYA ◽  
TAISUKE SATO
Keyword(s):  
Programming Languages ◽  
Programming Language ◽  
Expectation Maximization ◽  
Statistical Models ◽  
Operational Semantics ◽  
Probabilistic Logic ◽  
Parameter Learning ◽  
Rewrite Rules ◽  
High Level ◽  
Distribution Semantics

AbstractPRISM is an extension of Prolog with probabilistic predicates and built-in support for expectation-maximization learning. Constraint Handling Rules (CHR) is a high-level programming language based on multi-headed multiset rewrite rules.In this paper, we introduce a new probabilistic logic formalism, called CHRiSM, based on a combination of CHR and PRISM. It can be used for high-level rapid prototyping of complex statistical models by means of “chance rules”. The underlying PRISM system can then be used for several probabilistic inference tasks, including probability computation and parameter learning. We define the CHRiSM language in terms of syntax and operational semantics, and illustrate it with examples. We define the notion of ambiguous programs and define a distribution semantics for unambiguous programs. Next, we describe an implementation of CHRiSM, based on CHR(PRISM). We discuss the relation between CHRiSM and other probabilistic logic programming languages, in particular PCHR. Finally, we identify potential application domains.

scholarly journals Well–definedness and efficient inference for probabilistic logic programming under the distribution semantics

2012 ◽  
Vol 13 (2) ◽  
pp. 279-302 ◽  
Author(s):  
FABRIZIO RIGUZZI ◽  
TERRANCE SWIFT
Keyword(s):  
Probability Theory ◽  
Logic Programming ◽  
Probabilistic Inference ◽  
Probabilistic Logic ◽  
Logic Programs ◽  
Efficient Procedure ◽  
Probabilistic Logic Programming ◽  
Execution Times ◽  
Distribution Semantics

AbstractDistribution semantics is one of the most prominent approaches for the combination of logic programming and probability theory. Many languages follow this semantics, such as Independent Choice Logic, PRISM, pD, Logic Programs with Annotated Disjunctions (LPADs), and ProbLog. When a program contains functions symbols, the distribution semantics is well–defined only if the set of explanations for a query is finite and so is each explanation. Well–definedness is usually either explicitly imposed or is achieved by severely limiting the class of allowed programs. In this paper, we identify a larger class of programs for which the semantics is well–defined together with an efficient procedure for computing the probability of queries. Since Logic Programs with Annotated Disjunctions offer the most general syntax, we present our results for them, but our results are applicable to all languages under the distribution semantics. We present the algorithm “Probabilistic Inference with Tabling and Answer subsumption” (PITA) that computes the probability of queries by transforming a probabilistic program into a normal program and then applying SLG resolution with answer subsumption. PITA has been implemented in XSB and tested on six domains: two with function symbols and four without. The execution times are compared with those of ProbLog, cplint, and CVE. PITA was almost always able to solve larger problems in a shorter time, on domains with and without function symbols.

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