Computing a Probabilistic Extension of Answer Set Program Language Using ASP and Markov Logic Solvers

abstract: LPMLN is a recent probabilistic logic programming language which combines both Answer Set Programming (ASP) and Markov Logic. It is a proper extension of Answer Set programs which allows for reasoning about uncertainty using weighted rules under the stable model semantics with a weight scheme that is adopted from Markov Logic. LPMLN has been shown to be related to several formalisms from the knowledge representation (KR) side such as ASP and P-Log, and the statistical relational learning (SRL) side such as Markov Logic Networks (MLN), Problog and Pearl’s causal models (PCM). Formalisms like ASP, P-Log, Problog, MLN, PCM have all been shown to embeddable in LPMLN which demonstrates the expressivity of the language. Interestingly, LPMLN has also been shown to reducible to ASP and MLN which is not only theoretically interesting, but also practically important from a computational point of view in that the reductions yield ways to compute LPMLN programs utilizing ASP and MLN solvers. Additionally, the reductions also allow the users to compute other formalisms which can be reduced to LPMLN. This thesis realizes two implementations of LPMLN based on the reductions from LPMLN to ASP and LPMLN to MLN. This thesis first presents an implementation of LPMLN called LPMLN2ASP that uses standard ASP solvers for computing MAP inference using weak constraints, and marginal and conditional probabilities using stable models enumeration. Next, in this thesis, another implementation of LPMLN called LPMLN2MLN is presented that uses MLN solvers which apply completion to compute the tight fragment of LPMLN programs for MAP inference, marginal and conditional probabilities. The computation using ASP solvers yields exact inference as opposed to approximate inference using MLN solvers. Using these implementations, the usefulness of LPMLN for computing other formalisms is demonstrated by reducing them to LPMLN. The thesis also shows how the implementations are better than the native solvers of some of these formalisms on certain domains. The implementations make use of the current state of the art solving technologies in ASP and MLN, and therefore they benefit from any theoretical and practical advances in these technologies, thereby also benefiting the computation of other formalisms that can be reduced to LPMLN. Furthermore, the implementation also allows for certain SRL formalisms to be computed by ASP solvers, and certain KR formalisms to be computed by MLN solvers.Dissertation/ThesisMasters Thesis Computer Science 201

On the Relationships Among Probabilistic Extensions of Answer Set Semantics

abstract: Answer Set Programming (ASP) is one of the main formalisms in Knowledge Representation (KR) that is being widely applied in a large number of applications. While ASP is effective on Boolean decision problems, it has difficulty in expressing quantitative uncertainty and probability in a natural way. Logic Programs under the answer set semantics and Markov Logic Network (LPMLN) is a recent extension of answer set programs to overcome the limitation of the deterministic nature of ASP by adopting the log-linear weight scheme of Markov Logic. This thesis investigates the relationships between LPMLN and two other extensions of ASP: weak constraints to express a quantitative preference among answer sets, and P-log to incorporate probabilistic uncertainty. The studied relationships show how different extensions of answer set programs are related to each other, and how they are related to formalisms in Statistical Relational Learning, such as Problog and MLN, which have shown to be closely related to LPMLN. The studied relationships compare the properties of the involved languages and provide ways to compute one language using an implementation of another language. This thesis first presents a translation of LPMLN into programs with weak constraints. The translation allows for computing the most probable stable models (i.e., MAP estimates) or probability distribution in LPMLN programs using standard ASP solvers so that the well-developed techniques in ASP can be utilized. This result can be extended to other formalisms, such as Markov Logic, ProbLog, and Pearl’s Causal Models, that are shown to be translatable into LPMLN. This thesis also presents a translation of P-log into LPMLN. The translation tells how probabilistic nonmonotonicity (the ability of the reasoner to change his probabilistic model as a result of new information) of P-log can be represented in LPMLN, which yields a way to compute P-log using standard ASP solvers or MLN solvers.Dissertation/ThesisMasters Thesis Computer Science 201

plingo: A system for probabilistic reasoning in clingo based on lpmln

We present plingo, an extension of the ASP system clingo with various probabilistic reasoning modes. Plingo is centered upon LP^MLN, a probabilistic extension of ASP based on a weight scheme from Markov Logic. This choice is motivated by the fact that the core probabilistic reasoning modes can be mapped onto optimization problems and that LP^MLN may serve as a middle-ground formalism connecting to other probabilistic approaches. As a result, plingo offers three alternative frontends, for LP^MLN, P-log, and ProbLog. The corresponding input languages and reasoning modes are implemented by means of clingo's multi-shot and theory solving capabilities. The core of plingo amounts to a re-implementation of LP^MLN in terms of modern ASP technology, extended by an approximation technique based on a new method for answer set enumeration in the order of optimality. We evaluate plingo's performance empirically by comparing it to other probabilistic systems

Probabilistic Action Language pBC+

We present an ongoing research on a probabilistic extension of action language BC+. Just like BC+ is defined as a high-level notation of answer set programs for describing transition systems, the proposed language, which we call pBC+, is defined as a high-level notation of LP^{MLN} programs - a probabilistic extension of answer set programs. As preliminary results accomplished, we illustrate how probabilistic reasoning about transition systems, such as prediction, postdiction, and planning problems, as well as probabilistic diagnosis for dynamic domains, can be modeled in pBC+ and computed using an implementation of LP^{MLN}. For future work, we plan to develop a compiler that automatically translates pBC+ description into LP^{MLN} programs, as well as parameter learning in probabilistic action domains through LP^{MLN} weight learning. We will work on defining useful extensions of pBC+ to facilitate hypothetical/counterfactual reasoning. We will also find real-world applications, possibly in robotic domains, to empirically study the performance of this approach to probabilistic reasoning in action domains