We also prove that Hyper Hoare Logic is sound and complete. In fact, we prove that Hyper Hoare Logic subsumes the properties handled by numerous existing correctness and incorrectness logics, and can express hyperproperties that no existing Hoare logic can. By allowing assertions to reason about sets of states, Hyper Hoare Logic can reason about both the absence and the existence of (combinations of) executions, and, thereby, supports both proving and disproving program (hyper-)properties within the same logic. 3, formula 6, where subsumes is defined as x(x) (x) 3. The resulting logic is simple yet expressive: its judgments can express arbitrary trace- and hyperproperties over the terminating executions of a program. Guarino and Welty state that if is anti-rigid and is rigid then cant subsume. In this paper, we present Hyper Hoare Logic, a generalization of Hoare logic that lifts assertions to properties of arbitrary sets of states. All of these logics have in common that they specify program properties using assertions over a fixed number of states, for instance, a single pre- and post-state for functional properties or pairs of pre- and post-states for non-interference. On the other hand, program logics similar to Hoare logic have been proposed to disprove program properties (e.g., Incorrectness Logic), by proving the existence of (bad combinations of) executions. These program logics prove the absence of (bad combinations of) executions. While the LCS generalizes from examples that take the. On the one hand, Hoare logic has been generalized to prove properties of multiple executions of a program (so-called hyperproperties, such as determinism or non-interference). We study two forms of least general generalizations in description logic, the least common subsumer (LCS) and most specific concept (MSC). subsumption) non-conjunctive concepts C which system-subsume A, do not. Traditional Hoare logics prove properties of individual program executions (so-called trace properties, such as functional correctness). of deriving those logical consequences suitable for natural language presentation.

Hoare logics are proof systems that allow one to formally establish properties of computer programs.

Subsume logic