First-Order Stable Model Semantics with Intensional Functions

In classical logic, nonBoolean fluents, such as the location of an object, can be naturally described by functions. However, this is not the case in answer set programs, where the values of functions are pre-defined, and nonmonotonicity of the semantics is related to minimizing the extents of predicates but has nothing to do with functions. We extend the first-order stable model semantics by Ferraris, Lee, and Lifschitz to allow intensional functions -- functions that are specified by a logic program just like predicates are specified. We show that many known properties of the stable model semantics are naturally extended to this formalism and compare it with other related approaches to incorporating intensional functions. Furthermore, we use this extension as a basis for defining Answer Set Programming Modulo Theories (ASPMT), analogous to the way that Satisfiability Modulo Theories (SMT) is defined, allowing for SMT-like effective first-order reasoning in the context of ASP. Using SMT solving techniques involving functions, ASPMT can be applied to domains containing real numbers and alleviates the grounding problem. We show that other approaches to integrating ASP and CSP/SMT can be related to special cases of ASPMT in which functions are limited to non-intensional ones.Comment: 69 page

Analysing system behaviour by automatic benchmarking of system-level provenance

Provenance is a term originating from the work of art. It aims to provide a chain of information of a piece of arts from its creation to the current status. It records all the historic information relating to this piece of art, including the storage locations, ownership, buying prices, etc. until the current status. It has a very similar definition in data processing and computer science. It is used as the lineage of data in computer science to provide either reproducibility or tracing of activities happening in runtime for a different purpose. Similar to the provenance used in art, provenance used in computer science and data processing field describes how a piece of data was created, passed around, modified, and reached the current state. Also, it provides information on who is responsible for certain activities and other related information. It acts as metadata on components in a computer environment. As the concept of provenance is to record all related information of some data, the size of provenance itself is generally proportional to the amount of data processing that took place. It generally tends to be a large set of data and is hard to analyse. Also, in the provenance collecting process, not all information is useful for all purposes. For example, if we just want to trace all previous owners of a file, then all the storage location information may be ignored. To capture useful information and without needing to handle a large amount of information, researchers and developers develop different provenance recording tools that only record information needed by particular applications with different means and mechanisms throughout the systems. This action allows a lighter set of information for analysis but it results in non-standard provenance information and general users may not have a clear view on which tools are better for some purposes. For example, if we want to identify if certain action sequences have been performed in a process and who is accountable for these actions for security analysis, we have no idea which tools should be trusted to provide the correct set of information. Also, it is hard to compare the tools as there is not much common standard around. With the above need in mind, this thesis concentrate on providing an automated system ProvMark to benchmark the tools. This helps to show the strengths and weaknesses of their provenance results in different scenarios. It also allows tool developers to verify their tools and allows end-users to compare the tools at the same level to choose a suitable one for the purpose. As a whole, the benchmarking based on the expressiveness of the tools on different scenarios shows us the right choice of provenance tools on specific usage

Datalog Programs and Their Stable Models

Abstract. This paper is about the functionality of software systems used in answer set programming (ASP). ASP languages are viewed here, in the spirit of Datalog, as mechanisms for characterizing intensional (output) predicates in terms of extensional (input) predicates. Our approach to the semantics of ASP programs is based on the concept of a stable model defined in terms of a modification of parallel circumscription.