A Generic Framework for Implicate Generation Modulo Theories

Abstract

The clausal logical consequences of a formula are called its implicates. The generation of these implicates has several applications, such as the identification of missing hypotheses in a logical specification. We present a procedure that generates the implicates of a quantifierfree formula modulo a theory. No assumption is made on the considered theory, other than the existence of a decision procedure. The algorithm has been implemented (using the solvers MiniSAT, CVC4 and Z3) and experimental results show evidence of the practical relevance of the proposed approach.

Ilinva: Using Abduction to Generate Loop Invariants

“…We use the procedure GPiD described in [14] to generate A-implicants. A simplified version of this procedure is presented in Algorithm 1.…”

“…Compared to [14], details that are irrelevant for the purpose of the present paper are skipped and the procedure has been adapted to generate A-implicants instead of implicates (implicants and implicates are dual notions).…”

“…The first one is Why3 (see, e.g., http://why3.lri.fr/ or [16]), a well-known and widely-used platform for deductive program verification that is used to compute verification conditions and verify assertions. The second system, GPiD, is designed to generate implicants 1 of quantifier-free formulas modulo theories [14]. This system is used as an abductive reasoning procedure, thanks to the following property: if φ |= ψ, finding a hypothesis φ ′ such that φ ∧ φ ′ |= ψ is equivalent to finding φ ′ such that φ ′ |= φ ⇒ ψ. GPiD is generic, since it only relies on the existence of a decision procedure for the considered theory (counter-examples are exploited when available to speed-up the generation of the implicants when available).…”

“…The method is generic, i.e., it applies to a large set of programming languages and application domains; and lazy, in the sense that it only generates invariants that allow one to derive the required properties. It relies on an existing system called GPiD for abductive reasoning modulo theories [14], and on the platform for program verification Why3 [16]. Experiments show evidence of the practical relevance of our approach.…”

Signature-Based Abduction for Expressive Description Logics

“…Constraining hypotheses to those using only a set of allowed names, called abducibles, is a long-standing practice in abductive logic programming [Kakas, Kowalski, and Toni, 1992;Ray, 2009], and has recently also been investigated for first-order logic [Echenim, Peltier, and Tourret, 2017;Echenim, Peltier, and Sellami, 2018]. In the domain of DL knowledge bases, most research either does not consider abducibles, or only in restricted forms.…”