Logics Modulo Theories: a logical framework for multi-agent systems

Logics Modulo Theories (LMT) is a methodology for putting together logics that takes numbers of logics, each working in their own locality (local logics) and allows them to communicate through a global system that has its own (global) logic. This makes it suitable for the study of multi-agent systems. The original motivation for LMT comes from a consideration of agents working in their own domains or localities and then communicating with one another at a higher level. At the base are local worlds each with their own logic. Above them is a logic that takes statements from the local worlds and combines them. The two layers are connected by rules for transferring between local and global logics—in both directions. It will be made clear that aside from LMT’s applicability to agent systems, it can be applied to the area of ontology reconciliation, combining logics and which can subsume Satisfaction Modulo Theories (SMT), a technique for solving constraint satisfaction problems. To illustrate the layered logic approach of LMT, we give a number of very different examples, ranging from standard classical logics to algebraic specifications, where we have agents in contexts with local ontologies. Although we only consider two layers in the present article, we see no reason why the approach should not be extended to any finite number of tiers. In practice, to mechanize our systems, instead of using first-order logic one might use PROLOG, or another logic programming language in a very straightforward way. The following are the theses of this article: (i) when used for combining logics for multi-agent systems, in comparison to other methods LMT produces a more elegant and simpler logical system; (ii) the ideal properties of its component logics, namely, soundness and completeness, readily transfer to the resulting logic (under certain common conditions); and (iii) the proofs for these results are very straightforward because LMT uses well-established