Parsing in type logical grammars amounts to theorem proving in a substructural logic. This paper takes the proof net presentation of Lambek’s associative calculus as a case study. It introduces switch graphs for online maintenance of the Danos-Regnier acyclicity condition on proof nets. Early detection of Danos-Regnier acyclicity violations supports early failure in shift-reduce parsers. Normal...

Many knowledge representation tasks involve trees or similar structures as abstract datatypes. However, devising compact and efficient declarative representations of such structural properties is non-obvious and can be challenging indeed. In this paper, we take a number of acyclicity properties into consideration and investigate various logic-based approaches to encode them. We use answer set p...

We develop the theory of agrarian invariants, which are algebraic counterparts to $L^2$-invariants. Specifically, we introduce notions Betti numbers, acyclicity, torsion and polytope for finite free $G$-CW-co

The disjunctive skolem chase is a sound, complete, and potentially non-terminating procedure for solving boolean conjunctive query entailment over knowledge bases of existential rules. We develop novel acyclicity cyclicity notions this procedure; that is, we sufficient conditions to determine termination non-termination. Our empirical evaluation shows our are significantly more general than exi...

A walk W in edge-colored graph is called properly colored (PC) if every pair of consecutive edges in W is of different color. We study five types of PC acyclicity in edge-colored graphs such that graphs of PC acyclicity of type i is a proper superset of graphs of acyclicity of type i+1, i = 1, 2, 3, 4. The first three types are equivalent to the absence of PC cycles, PC trails, and PC walks. Wh...