Abduction of Linear Arithmetic Constraints

Exact soultion of full interval linear equation AX=B based on Kaucher arithmetic

Solving Sparse Linear Constraints

Linear arithmetic decision procedures form an important part of theorem provers for program verification. In most verification benchmarks, the linear arithmetic constraints are dominated by simple difference constraints of the form x ≤ y + c. Sparse linear arithmetic (SLA) denotes a set of linear arithmetic constraints with a very few non-difference constraints. In this paper, we propose an eff...

Computing a Complete Basis for Equalities Implied by a System of LRA Constraints

We present three new methods that investigate the equalities implied by a system of linear arithmetic constraints. Implied equalities can be used to simplify linear arithmetic constraints and are valuable in the context of Nelson-Oppen style combinations of theories. The first method efficiently checks whether a system of linear arithmetic constraints implies an equality at all. In case the sys...

HYPROLOG: A New Logic Programming Language with Assumptions and Abduction

We present HYPROLOG, a novel integration of Prolog with assumptions and abduction which is implemented in and partly borrows syntax from Constraint Handling Rules (CHR) for integrity constraints. Assumptions are a mechanism inspired by linear logic and taken over from Assumption Grammars. The language shows a novel flexibility in the interaction between the different paradigms, including all ad...

Two Transformations of Clauses into Constraints and Their Properties for Cost-Based Hypothetical Reasoning

This paper describes two ways to transform propositional clauses into mathematical constraints, and gives an overview of mathematical optimization approaches to inference. The first transformation, which translates constraints into linear inequalities, has been applied to cost-based abduction in the past and showed good performance. The second one, which produces nonlinear equalities, is common...