Efficient Constraints on Possible Worlds for Reasoning about Necessity

Modal logics offer natural, declarative representations for describing both the modular structure of logical specifications and the attitudes and behaviors of agents. The results of this paper further the goal of building practical, efficient reasoning systems using modal logics. The key problem in modal deduction is reasoning about the world in a model (or scope in a proof) at which an inference rule is applied—a potentially hard problem. This paper investigates the use of partial-order mechanisms to maintain constraints on the application of modal rules in proof search in restricted languages. The main result is a simple, incremental polynomial-time algorithm to correctly order rules in proof trees for combinations of K, K4, T and S4 necessity operators governed by a variety of interactions, assuming an encoding of negation using a scoped constant ┴. This contrasts with previous equational unification methods, which have exponential performance in general because they simply guess among possible intercalations of modal operators. The new, fast algorithm is appropriate for use in a wide variety of applications of modal logic, from planning to logic programming

Association of Christians in the Mathematical Sciences Proceedings 2019

The conference proceedings of the Association of Christians in the Mathematical Sciences biannual conference, May 29-June 1, 2019 at Indiana Wesleyan University

Logical Foundations of Object-Oriented and Frame-Based Languages

We propose a novel logic, called Frame Logic (abbr., F-logic), that accounts in a clean, declarative fashion for most of the structural aspects of object-oriented and frame-based languages. These features include object identity, complex objects, inheritance, polymorphic types, methods, encapsulation, and others. In a sense, F-logic stands in the same relationship to the object-oriented paradigm as classical predicate calculus stands to relational programming. The syntax of F-logic is higher-order, which, among other things, allows the user to explore data and schema using the same declarative language. F-logic has a model-theoretic semantics and a sound and complete resolution-based proof procedure. This paper also discusses various aspects of programming in declarative object-oriented languages based on F-logic