Abstract In the field of formal verification, certifying proofs serve as compelling evidence to demonstrate the correctness of a model within a deductive system. These proofs can be automatically generated as a by-product of the verification process and are key artifacts for high-assurance systems. Their significance lies in their ability to be independently verified by proof checkers, which provides a more convenient approach than certifying the tools that generate them. Modern model checking algorithms adopt deductive methods and usually generate proofs in terms of inductive invariants, assuming that these apply to the original system under verification. Model checkers, though, often make use of a range of complex pre-processing simplifications and transformations to ease the verification process, which add another layer of complexity to the generation of proofs. In this paper, we present a novel approach for certifying model checking results exploiting a theorem prover and a theory of temporal deductive rules that can support various kinds of transformations and simplification of the original circuit. We implemented and experimentally evaluated our contribution on invariants generated using two state-of-the-art model checkers, nuXmv and PdTRAV, and by defining a set of rules within a theorem prover, to validate each certificate.

The paper presents a spatio-temporal ontology guided by a particular methodology, in which the semantics is constructed within a spatio-temporal interpretation structure that is built up in three stages. The first, stage stipulates a standard classical model of time and space. This structure forms the grounding for the interpretation. The next stage is the specification of domains of entities, which are either elements of the grounding structure (time points and regions) or constructions from these elements (mappings from time to space associated with individuals existing within the spatio-temporal structure). The final stage is the definition of conceptual vocabulary in terms of the grounding structure and the specified domains. This definitional stage can be further subdivided into three types of specification: direct grounding of primitives onto the underlying structure, indirect grounding by defining additional vocabulary in terms of grounded primitives, partial grounding by specifying semantics types and axioms to constrain the meaning of vocabulary that is not explicitly defined. The main goal of the paper is to advocate a methodology rather than a specific ontology. We suggest that building up in this way, results in robust ontologies, whose assumptions can be clearly seen, since they are encapsulated within the grounding stage and domain specifications. Although the definitional stage may incorporate a diverse and expressive vocabulary, its terms are essentially just labels for properties and relations that were already implicit within the grounding structure.

We consider a modal logic based on mathematical morphology which allows the expression of mereotopological relations between subgraphs in the setting of the discrete space. A specific form of topological closure for graphs can be expressed in the logic, as a combination of the negation and its bi-intuitionistic dual, as well as a modality, using the stable relation Q, which describes the incidence structure of the graph. By working in this context we have been able to define qualitative spatial relations between discrete regions, and to compare them with earlier works in mereotopology, both in the discrete and in the continuous space.