Property specification patterns (PSPs) have been proposed to ease the formalization of requirements, yet enable automated verification thereof. In particular, the internal consistency of specifications written with PSPs can be checked automatically with the use of, for example, linear temporal logic (LTL) satisfiability solvers. However, for most practical applications, the expressiveness of PSPs is too restricted to enable writing useful requirement specifications, and proving that a set of requirements is inconsistent can be worthless unless a minimal set of conflicting requirements is extracted to help designers to correct a wrong specification. In this paper, we extend PSPs by considering Boolean as well as atomic numerical assertions, we contribute an encoding from extended PSPs to LTL formulas, and we present an algorithm computing inconsistency explanations, i.e., irreducible inconsistent subsets of the original set of requirements. Our extension enables us to reason about the internal consistency of functional requirements which would not be captured by basic PSPs. Experimental results demonstrate that our approach can check and explain (in)consistencies in specifications with nearly two thousand requirements generated using a probabilistic model, and that it enables effective handling of real-world case studies
