Alexander V. Gheorghiu

Alexander V. Gheorghiu, Yll Buzoku

The field of proof-theoretic semantics (P-tS) offers an alternative approach to meaning in logic that is based on inference and argument (rather than truth in a model). It has been successfully developed for various logics; in particular, Sandqvist has developed such semantics for both classical and intuitionistic logic. In the case of classical logic, P-tS provides a conception of consequence that avoids an a priori commitment to the principle of bivalence, addressing what Dummett identified as a significant foundational challenge in logic. In this paper, we propose an alternative P-tS for classical logic, which essentially extends the P-tS for intuitionistic logic by operating over literals rather than atomic propositions. Importantly, literals are atomic and not defined by negation but are related by a primitive duality encoded inferentially at the atomic level. This semantics illustrates the perspective that classical logic can be understood as intuitionistic logic supplemented by a principle of duality, offering fresh insights into the relationship between these two systems.

Alexander V. Gheorghiu

Existing methods for verifying access control policies require the policy to be complete and fully determined before verification can proceed, but in practice policies are developed iteratively, composed from independently maintained components, and extended as organisational structures evolve. We introduce robust property verification: the problem of determining what a policy's structure commits it to regardless of how pending decisions are resolved and regardless of subsequent extension. We define a support judgment $\Vdash_{P}ϕ$ stating that policy $P$ has robust property $ϕ$, with connectives for implication, conjunction, disjunction, and negation, prove that it is compositional (verified properties persist under policy extension by a monotonicity theorem), and show that despite quantifying universally over all possible policy extensions the judgment reduces to proof search in a second-order logic programming language. Soundness and completeness of this reduction are established, yielding a finitary and executable verification procedure for robust security properties.

Alexander V. Gheorghiu

Sandqvist's base-extension semantics for intuitionistic propositional logic defines a support relation parametrised by atomic bases, with validity identified as support in every base. Sandqvist's completeness theorem answers the global question: which formulae are valid? This paper addresses the local question: given a fixed base, what does support in that base correspond to? We show that support in a fixed base coincides with proof-search in a second-order hereditary Harrop logic program, via an encoding of formulae as logic-programming goals. This encoding proceeds by reading the semantic clauses in continuation-passing style, revealing that the universal quantifiers over base extensions and atoms appearing in those clauses are not domain-ranging quantifiers over a completed totality, but eigenvariables governed by a standard freshness discipline. Base-extension semantics thereby admits a fully constructive and computationally transparent interpretation: support is proof-search. The result complements Sandqvist's global theorem with a local correspondence, vindicates the anti-realist foundations of the framework on its own terms, and opens the way for implementing the semantics in modelling tasks.