Shahab Tasharrofi

A semantic account for modularity in multi-language modelling of search problems

Motivated by the need to combine systems and logics, we develop a modular approach to the model expansion (MX) problem, a task which is common in applications such as planning, scheduling, computational biology, formal verification. We develop a modular framework where parts of a modular system can be written in different languages. We start our development from a previous work, [14], but modify and extend that framework significantly. In particular, we use a model-theoretic setting and introduce a feedback (loop) operator on modules. We study the expressive power of our framework and demonstrate that adding the feedback operator increases the expressive power considerably. We prove that, even with individual modules being polytime solvable, the framework is expressive enough to capture all of NP, a property which does not hold without loop. Moreover, we demonstrate that, using monotonicity and anti-monotonicity of modules, one can significantly reduce the search space of a solution to a modular system.

Enfragmo: a system for modelling and solving search problems with logic

In this paper, we present the Enfragmo system for specifying and solving combinatorial search problems. It supports natural specification of problems by providing users with a rich language, based on an extension of first order logic. Enfragmo takes as input a problem specification and a problem instance and produces a propositional CNF formula representing solutions to the instance, which is sent to a SAT solver. Because the specification language is high level, Enfragmo provides combinatorial problem solving capability to users without expertise in use of SAT solvers or algorithms for solving combinatorial problems. Here, we describe the specification language and implementation of Enfragmo, and give experimental evidence that its performance is comparable to that of related systems.

PBINT, a logic for modelling search problems involving arithmetic

Motivated by computer science challenges, Gradel and Gurevich [13] suggested to extend the approach and methods of finite model theory beyond finite structures, an approach they called Metafinite Model Theory. We develop this direction further, in application to constraint specification/modelling languages. Following [27], we use a framework based on embedded model theory, but with a different background structure, the structure of arithmetic which contains at least (N; 0, 1, +, ×, <, ∥ ∥), where ∥x∥ returns the size of the binary encoding of x. We prove that on these structures, we can unconditionally capture NP using a variant of a guarded logic. This improves the result of [27] (and thus indirectly [13]) by eliminating the small cost condition on input structures. As a consequence, our logic (an idealized specification language) allows one to represent common arithmetical problems such as integer factorization or disjoint scheduling naturally, with built-in arithmetic, as opposed to using a binary encoding. Thus, this result gives a remedy to a problem with practical specification languages, namely that there are common arithmetical problems that can be decided in NP but cannot be axiomatized naturally in current modelling languages. We give some examples of such axiomatizations in PBINT and explain how our result applies to constraint specification/modelling languages.

Speed-up techniques for negation in grounding

Grounding is the task of reducing a first order formula to ground formula that is equivalent on a given universe, and is important in many kinds of problem solving and reasoning systems. One method for grounding is based on an extension of the relational algebra, exploiting the fact that grounding over a given domain is similar to query answering. In this paper, we introduce two methods for speeding up algebraic grounding by reducing the size of tables produced. One method employs rewriting of the formula before grounding, and the other uses a further extension of the algebra that makes negation efficient.We have implemented the methods, and present experimental evidence of their effectiveness.

Solving Modular Model Expansion: Case Studies

Model expansion task is the task of representing the essence of search problems where we are given an instance of a problem and are searching for a solution satisfying certain properties. Such tasks are common in AI planning, scheduling, logistics, supply chain management, etc., and are inherently modular. Recently, the model expansion framework was extended to deal with multiple modules to represent e.g. the task of constructing a logistics service provider relying on local service providers. In the current paper, we study existing systems that operate in a modular way in order to obtain general principles of solving modular model expansion tasks. We introduce a general algorithm to solve model expansion tasks for modular systems. We demonstrate, through several case studies, that our algorithm closely corresponds to what is done in practice in different areas such as Satisfiability Modulo Theories (SMT), Integer Linear Programming (ILP), and Answer Set Programming (ASP). We make our framework language-independent through a model-theoretic development.

User Modeling Using Network Layer Information

The emerging growth of computer networks and the great influence of Internet on various aspects of trade made using users’ information to improve the performance of systems an ordinary task. Currently almost all the user modeling frameworks catch the required information from the application layer, thus just the information providers could use them. As a result, these frameworks have no benefit for the inbetween nodes such as ISPs which may access these data in network layer. In this paper we propose a new multi-agent framework which can be used for modeling the users by network layer information. This framework can help the in-between nodes to arrange their service policies based on different user models. Although using intelligent agents and artificial intelligence techniques, the framework extracts the hidden relations between network layer behavior components and application layer behavior components, thus improving the modeling performance. Moreover we have presented a case study which models an ordinary ISP’s users and shows how the model can be used to improve the ISP’s quality of service.