Solving Modular Model Expansion: Case Studies

Abstract

The work we describe here is a part of a research program of developing foundations of declarative solving of search problems. We consider the model expansion task as the task 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 artificial intelligence, formal verification, computational biology. Recently, the model expansion framework was extended to deal with multiple modules. In the current paper, inspired by practical combined solvers, we introduce an algorithm to solve model expansion tasks for modular systems. We show that our algorithm closely corresponds to what is done in practice in different areas such as Satisfiability Modulo Theories (SMT), Integer Linear Programming (ILP), Answer Set Programming (ASP).

On abstract modular inference systems and solvers

“…Tasharrofi, Wu, and Ternovska [25] developed and studied an algorithm for processing modular model expansion tasks in the abstract multi-logic system concept developed by Tasharrofi and Ternovska [24]. They use the traditional pseudocode method to present the developed algorithm.…”

An Algebra of Combined Constraint Solving

“…(We limit ourselves to intuitions and do not give any precise propositions or theorems here, since it is only a project description paper). The operations we introduce in (7) subsume those we used in previous work [19,20,21,22,23,24,25]. In particular, concatenation here is exactly like sequential composition we used before, and feedback is definable using selection, where an input is equated with an output.…”

“…Shahab also proposed the term "meta-solving" in a recent discussion. Instantiations of the algorithm [18] were shown to capture the work of SMT (DPPL(T)), ASP-CP, IDP, ILP (represented as modular systems) in [46], and in Xiongnan (Newman) Wu's thesis [20]. An important future research direction is to explain good algorithmic properties of various fragments of the dynamic version of the algebra, and to explore those properties in algorithms for meta-solving.…”

“…We consider the dynamic version very important because it formalizes a typical task in hybrid multi-language constraint solving, and has good computational properties. Modular systems representing SMT, branch-and-cut based ILP, ASP-CP combinations are given in [20,21] to illustrate a high-level algorithm [18] for solving modular systems (what we now call meta-solving).…”

“…In this paper, we continue the line of research we started in [18] where Modular Systems were introduced. They were further developed in [19,20,21,22,23,24,25,26]. The main conceptual shift proposed in those works was to take model-theoretic approach seriously.…”