On the Semantics of Gringo

Input languages of answer set solvers are based on the mathematically simple concept of a stable model. But many useful constructs available in these languages, including local variables, conditional literals, and aggregates, cannot be easily explained in terms of stable models in the sense of the original definition of this concept and its straightforward generalizations. Manuals written by designers of answer set solvers usually explain such constructs using examples and informal comments that appeal to the user's intuition, without references to any precise semantics. We propose to approach the problem of defining the semantics of gringo programs by translating them into the language of infinitary propositional formulas. This semantics allows us to study equivalent transformations of gringo programs using natural deduction in infinitary propositional logic.Comment: Proceedings of Answer Set Programming and Other Computing Paradigms (ASPOCP 2013), 6th International Workshop, August 25, 2013, Istanbul, Turke

On Equivalence of Infinitary Formulas under the Stable Model Semantics

Propositional formulas that are equivalent in intuitionistic logic, or in its extension known as the logic of here-and-there, have the same stable models. We extend this theorem to propositional formulas with infinitely long conjunctions and disjunctions and show how to apply this generalization to proving properties of aggregates in answer set programming. To appear in Theory and Practice of Logic Programming (TPLP)

Representing, reasoning and answering questions about biological pathways - various applications

Biological organisms are composed of numerous interconnected biochemical processes. Diseases occur when normal functionality of these processes is disrupted. Thus, understanding these biochemical processes and their interrelationships is a primary task in biomedical research and a prerequisite for diagnosing diseases, and drug development. Scientists studying these processes have identified various pathways responsible for drug metabolism, and signal transduction, etc. Newer techniques and speed improvements have resulted in deeper knowledge about these pathways, resulting in refined models that tend to be large and complex, making it difficult for a person to remember all aspects of it. Thus, computer models are needed to analyze them. We want to build such a system that allows modeling of biological systems and pathways in such a way that we can answer questions about them. Many existing models focus on structural and/or factoid questions, using surface-level knowledge that does not require understanding the underlying model. We believe these are not the kind of questions that a biologist may ask someone to test their understanding of the biological processes. We want our system to answer the kind of questions a biologist may ask. Such questions appear in early college level text books. Thus the main goal of our thesis is to develop a system that allows us to encode knowledge about biological pathways and answer such questions about them demonstrating understanding of the pathway. To that end, we develop a language that will allow posing such questions and illustrate the utility of our framework with various applications in the biological domain. We use some existing tools with modifications to accomplish our goal. Finally, we apply our system to real world applications by extracting pathway knowledge from text and answering questions related to drug development.Comment: thesi