On Irrelevant Literals in Pseudo-Boolean Constraint Learning

On Quantifying Literals in Boolean Logic and Its Applications to Explainable AI

Quantified Boolean logic results from adding operators to Boolean logic for existentially and universally quantifying variables. This extends the reach of Boolean logic by enabling a variety of applications that have been explored over the decades. The existential quantification of literals (variable states) and its applications have also been studied in the literature. In this paper, we complement this by studying universal literal quantification and its applications, particularly to explainable AI. We also provide a novel semantics for quantification, discuss the interplay between variable/l…

Boolean Equi-propagation for Concise and Efficient SAT Encodings of Combinatorial Problems

We present an approach to propagation-based SAT encoding of combinatorial problems, Boolean equi-propagation, where constraints are modeled as Boolean functions which propagate information about equalities between Boolean literals. This information is then applied to simplify the CNF encoding of the constraints. A key factor is that considering only a small fragment of a constraint model at one time enables us to apply stronger, and even complete, reasoning to detect equivalent literals in that fragment. Once detected, equivalences apply to simplify the entire constraint model and facilitate f…

Complexity assessments for decidable fragments of Set Theory. IV: A quadratic reduction of constraints over nested sets to Boolean formulae

As a contribution to quantitative set-theoretic inferencing, a translation is proposed of conjunctions of literals of the forms $x=y\setminus z$, $x \neq y\setminus z$, and $z =\{x\}$, where $x,y,z$ stand for variables ranging over the von Neumann universe of sets, into unquantified Boolean formulae of a rather simple conjunctive normal form. The formulae in the target language involve variables ranging over a Boolean ring of sets, along with a difference operator and relators designating equality, non-disjointness and inclusion. Moreover, the result of each translation is a conjunction of lit…

Implementing a Relevance Tracker Module

PC(ID) extends propositional logic with inductive definitions: rule sets under the well-founded semantics. Recently, a notion of relevance was introduced for this language. This notion determines the set of undecided literals that can still influence the satisfiability of a PC(ID) formula in a given partial assignment. The idea is that the PC(ID) solver can make decisions only on relevant literals without losing soundness and thus safely ignore irrelevant literals. One important insight that the relevance of a literal is completely determined by the current solver state. During search, the sol…

伪布尔传播的新混合启发式方法

New Hybrid Heuristics for Pseudo-Boolean Propagation

本文提出了一种新的混合启发式方法，用于改进伪布尔传播中的单位传播策略，以在RoundingSAT求解器中取得更好的性能。

PBCounter：伪布尔公式上的加权模型计数

PBCounter: Weighted Model Counting on Pseudo-Boolean Formulas

针对CNF表示不自然的问题，提出在表达能力更强的伪布尔公式上执行加权模型计数，基于ADDMC框架实现工具PBCounter，实验表明其优于现有CNF计数器。