We introduce novel mathematical models and algorithms to generate (shortest or k different) explanations for biomedical queries, using answer set programming. We implement these algorithms and integrate them in BioQuery-ASP. We illustrate the usefulness of these methods with some complex biomedical queries related to drug discovery, over the biomedical knowledge resources PharmGKB, DrugBank, BioGRID, CTD, SIDER, Disease Ontology, and Orphadata.
@cite_10 , similar to our work, the question why is an atom @math in an answer set @math for an ASP program @math '' is studied. As an answer to this question, the authors of @cite_10 provide the rule in @math that supports @math with respect to @math ; whereas we compute shortest or @math different explanations (as a tree whose vertices are labeled by rules).
@cite_10
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The paper introduces the notion of offline justification for answer set programming (ASP). Justifications provide a graph-based explanation of the truth value of an atom with respect to a given answer set. The paper extends also this notion to provide justification of atoms during the computation of an answer set (on-line justification) and presents an integration of online justifications within the computation model of SMODELS. Offline and online justifications provide useful tools to enhance understanding of ASP, and they offer a basic data structure to support methodologies and tools for debugging answer set programs. A preliminary implementation has been developed in . In recent years, Answer Set Programming ASP, logic programming under the stable model or answer set semantics, has seen several extensions by generalizing the notion of an atom in these programs: be it aggregate atoms, HEX atoms, generalized quantifiers, or abstract constraints, the idea is to have more complicated satisfaction patterns in the lattice of Herbrand interpretations than traditional, simple atoms. In this paper we refer to any of these constructs as generalized atoms. It is known that programs with generalized atoms that have monotonic or antimonotonic satisfaction patterns do not increase complexity with respect to programs with simple atoms if satisfaction of the generalized atoms can be decided in polynomial time under most semantics. It is also known that generalized atoms that are nonmonotonic being neither monotonic nor antimonotonic can, but need not, increase the complexity by one level in the polynomial hierarchy if non-disjunctive programs under the FLP semantics are considered. In this paper we provide the precise boundary of this complexity gap: programs with convex generalized atom never increase complexity, while allowing a single non-convex generalized atom under reasonable conditions always does. We also discuss several implications of this result in practice. We investigate a generalization of weight-constraint programs with stable semantics, as implemented in the ASP solver smodels. Our programs admit atoms of the form ( X, F ) where X is a finite set of propositional atoms and ( F ) is an arbitrary family of subsets of X. We call such atoms set constaints and show that the concept of stable model can be generalized to programs admitting set constraints both in the bodies and the heads of clauses. Natural tools to investigate the fixpoint semantics for such programs are nondeterministic operators in complete lattices. We prove two fixpoint theorems for such operators. Solving algebraic word problems requires executing a series of arithmetic operations---a program---to obtain a final answer. However, since programs can be arbitrarily complicated, inducing them directly from question-answer pairs is a formidable challenge. To make this task more feasible, we solve these problems by generating answer rationales, sequences of natural language and human-readable mathematical expressions that derive the final answer through a series of small steps. Although rationales do not explicitly specify programs, they provide a scaffolding for their structure via intermediate milestones. To evaluate our approach, we have created a new 100,000-sample dataset of questions, answers and rationales. Experimental results show that indirect supervision of program learning via answer rationales is a promising strategy for inducing arithmetic programs.