Satisfiability of Short Circuit Logic

The logical connectives typically found in programming languages are similar to their mathematical counterparts, yet different due to their short-circuit behaviour – when evaluating them, the second argument is only evaluated if the first argument is not sufficient to determine the result. Combined with the possibility of side-effects, this creates a different type of logic called Short Circuit Logic. A greater theoretical understanding of this logic can lead to more efficient programming and faster program execution. In this thesis, formula satisfiability in the context of Short Circuit Logic is discussed. A formal definition of evaluation based on valuation algebras is presented, alongside an alternative definition based on valuation paths. The accompanying satisfiability and ‘path-satisfiability’ are then proven to be equivalent, and an implementation of pathsatisfiability is given. Although five types of valuation algebras can be discerned, there are only three corresponding types of valuation paths. From this, conclusions are drawn about satisfiability and side-effects; the manner in which side-effects alter truth values is relevant when analysing satisfiability, but the side-effects themselves are not. Title: Satisfiability of Short Circuit Logic Authors: Sander in ’t Veld, [email protected] Supervisors: dr. Inge Bethke, prof. dr. Jan van Eijck Date: October 20, 2015 Universiteit van Amsterdam Science Park 904, 1098 XH Amsterdam http://www.science.uva.nl