Translating P-log, LPMLN, LPOD, and CR-Prolog2 into Standard Answer Set Programs

Answer set programming (ASP) is a particularly useful approach for nonmonotonic reasoning in knowledge representation. In order to handle quantitative and qualitative reasoning, a number of different extensions of ASP have been invented, such as quantitative extensions LP^{MLN} and P-log, and qualitative extensions LPOD, and CR-Prolog_2. Although each of these formalisms introduced some new and unique concepts, we present reductions of each of these languages into the standard ASP language, which not only gives us an alternative insight into the semantics of these extensions in terms of the standard ASP language, but also shows that the standard ASP is capable of representing quantitative uncertainty and qualitative uncertainty. What\u27s more, our translations yield a way to tune the semantics of LPOD and CR-Prolog_2. Since the semantics of each formalism is represented in ASP rules, we can modify their semantics by modifying the corresponding ASP rules. For future work, we plan to create a new formalism that is capable of representing quantitative and qualitative uncertainty at the same time. Since LPOD rules are simple and informative, we will first try to include quantitative preference into LPOD by adding the concept of weight and tune the semantics of LPOD by modifying the translated standard ASP rules

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