arXiv subjects

Marianna Girlando

Publications and source records attributed to Marianna Girlando.

12 recordsLinked to original sources

arXiv2026

Library-Grade Modal Logic

Modal logic comprises a broad family of logics to reason about relational structures. The literature presents many such logics, displaying diverse operators, semantics, and applications. This plurality is reflected in a zoo of mechanised modal logics, which often duplicate syntax, semantics, metatheory, and reasoning infrastructure. We present a library-grade formalisation of modal logic in Lean, developed as part of CSLib (the Lean Computer Science Library) and designed around two complementary forms of reuse: vertical reuse, whereby specialised logics inherit from common abstractions, and horizontal reuse, whereby modal logic becomes a reasoning tool for independently formalised domains. Our development provides a generic framework for polyadic modal languages, reusable metatheory and proof automation, and derived interfaces for specialised modal logics. We exemplify our infrastructure by deriving basic modal logic, basic temporal logic, and Hennessy-Milner Logic; the latter subsumes and extends CSLib's previous implementation while reducing its logic-specific code by 67%. We further apply the same modal infrastructure to reasoning about mathematics (radicals of ideals), theory of programming languages (the type safety strategy for the simply typed $λ$-calculus), and concurrency theory (reasoning about processes in the Calculus of Communicating Systems). Our experience suggests that reuse, automation, and integration with the strong Lean ecosystem should be treated as first-class design concerns when formalising theories for shared libraries.

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arXiv2026

A decision procedure for intuitionistic modal logic IS4 (and IK4)

In this paper, we show that the two intuitionistic modal logics IS4 and IK4 are decidable. We provide a constructive decision procedure, that, given a formula, produces either a proof showing the formula to be valid or a finite countermodel falsifying the formula, thus also proving the finite model property for both logics. The main ingredient of our strategy is the introduction of (possibly unsound) loop rules, which encode repeating behaviour in proof search. This paper fixes a previous mistake in our LICS'23 contribution.

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arXiv2026

Labelled Sequent Calculi for Propositional Team Logics

Team semantics is a general framework where formulas are not interpreted with respect to a single point of evaluation, but with respect to sets of such points. Team semantics is used in dependence logic, to reason about dependencies between variables, and in inquisitive logic, to formalize the meaning of questions. We provide sound and complete labelled sequent calculi for four logics based on team semantics: basic inquisitive logic, propositional intuitionistic dependence logic, and their respective extensions with tensor disjunction. For technical reasons, we restrict ourselves to languages with finitely many propositional atoms. The rules of weakening, contraction and cut are shown to be admissible in each of our calculi. In the last part of the paper, we present terminating proof search procedures for variants of our proof systems, in which labels have a simplified structure.

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arXiv2026

Proceedings of the Sixteenth International Conference on Advances in Modal Logic

Advances in Modal Logic (AiML) was founded in 1995 as an initiative devoted to presenting an up-to-date picture of research in modal logic and its many applications. It combines a conference series with volumes arising from the conferences, and has become the flagship international forum for work on all aspects of modal logic. Over the past three decades, AiML has both recorded and helped shape developments across the field, bringing together semantic, proof-theoretic, algebraic, topological, computational, philosophical, and applied perspectives on modal and related logics. Exactly thirty years after the first AiML conference, AiML 2026, the sixteenth conference in the series, is organized by the Institute of Logic, Language and Computation (ILLC) of the University of Amsterdam. The conference takes place in Amsterdam, the Netherlands, from 29 June to 3 July 2026. This volume contains abstracts of invited talks and full papers accepted for the conference. Beginning with AiML 2026, the proceedings are published open access via Electronic Proceedings in Theoretical Computer Science (EPTCS).

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arXiv2025

A Proof-Theoretic View of Basic Intuitionistic Conditional Logic (Extended Version)

Intuitionistic conditional logic, studied by Weiss, Ciardelli and Liu, and Olkhovikov, aims at providing a constructive analysis of conditional reasoning. In this framework, the would and the might conditional operators are no longer interdefinable. The intuitionistic conditional logics considered in the literature are defined by setting Chellas' conditional logic CK, whose semantics is defined using selection functions, within the constructive and intuitionistic framework introduced for intuitionistic modal logics. This operation gives rise to a constructive and an intuitionistic variant of (might-free-) CK, which we call CCKbox and IntCK respectively. Building on the proof systems defined for CK and for intuitionistic modal logics, in this paper we introduce a nested calculus for IntCK and a sequent calculus for CCKbox. Based on the sequent calculus, we define CCK, a conservative extension of Weiss' logic CCKbox with the might operator. We introduce a class of models and an axiomatization for CCK, and extend these result to several extensions of CCK.

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arXiv2025

A Bi-nested Calculus for Intuitionistic K: Proofs and Countermodels

The logic IK is the intuitionistic variant of modal logic introduced by Fischer Servi, Plotkin and Stirling, and studied by Simpson. This logic is considered a fundamental intuitionstic modal system as it corresponds, modulo the standard translation, to a fragment of intuitionstic first-order logic. In this paper we present a labelled-free bi-nested sequent calculus for IK. This proof system comprises two kinds of nesting, corresponding to the two relations of bi-relational models for IK: a pre-order relation, from intuitionistic models, and a binary relation, akin to the accessibility relation of Kripke models. The calculus provides a decision procedure for IK by means of a suitable proof-search strategy. This is the first labelled-free calculus for IK which allows direct counter-model extraction: from a single failed derivation, it is possible to construct a finite countermodel for the formula at the root. We further show the bi-nested calculus can simulate both the (standard) nested calculus and labelled sequent calculus, which are two best known calculi proposed in the literature for IK.

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arXiv2025

Internal and External Calculi: Ordering the Jungle without Being Lost in Translations

This paper gives a broad account of the various sequent-based proof formalisms in the proof-theoretic literature. We consider formalisms for various modal and tense logics, intuitionistic logic, conditional logics, and bunched logics. After providing an overview of the logics and proof formalisms under consideration, we show how these sequent-based formalisms can be placed in a hierarchy in terms of the underlying data structure of the sequents. We then discuss how this hierarchy can be traversed using translations. Translating proofs up this hierarchy is found to be relatively straightforward while translating proofs down the hierarchy is substantially more difficult. Finally, we inspect the prevalent distinction in structural proof theory between 'internal calculi' and 'external calculi.' We discuss the ambiguities involved in the informal definitions of these categories, and we critically assess the properties that (calculi from) these classes are purported to possess.

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arXiv2025

A significance-based account of ceteris paribus counterfactuals

When evaluating a counterfactual statement, it is often convenient to specify conditions that ought to be kept unchanged. Formally, this can be done by associating to each counterfactual a ceteris paribus set of formulas, specifying the facts that "ought to be kept unchanged". Ceteris paribus counterfactuals originate in the debate between D. Lewis and Fine in the 1970s, and have been captured in formal accounts. However, these accounts are merely based on 'counting' formulas, and can yield counterintuitive results. In this paper, we develop a novel approach to evaluate ceteris paribus counterfactuals at (weakly) centered sphere models, by taking into account the 'significance' of formulas that ought to be kept unchanged. Hypothetical states that keep the most significant formulas unchanged will be prioritized in the evaluation of a counterfactual. We show that the resulting notion of validity coincides with theoremhood in Lewis' conditional logics VC or VW.

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arXiv2023

Intuitionistic S4 is decidable

In this paper we demonstrate decidability for the intuitionistic modal logic S4 first formulated by Fischer Servi. This solves a problem that has been open for almost thirty years since it had been posed in Simpson's PhD thesis in 1994. We obtain this result by performing proof search in a labelled deductive system that, instead of using only one binary relation on the labels, employs two: one corresponding to the accessibility relation of modal logic and the other corresponding to the order relation of intuitionistic Kripke frames. Our search algorithm outputs either a proof or a finite counter-model, thus, additionally establishing the finite model property for intuitionistic S4, which has been another long-standing open problem in the area.

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arXiv2022

Comparative plausibility in neighbourhood models: axiom systems and sequent calculi

We introduce a family of comparative plausibility logics over neighbourhood models, generalising Lewis' comparative plausibility operator over sphere models. We provide axiom systems for the logics, and prove their soundness and completeness with respect to the semantics. Then, we introduce two kinds of analytic proof systems for several logics in the family: a multi-premisses sequent calculus in the style of Lellmann and Pattinson, for which we prove cut admissibility, and a hypersequent calculus based on structured calculi for conditional logics by Girlando et al., tailored for countermodel construction over failed proof search. Our results constitute the first steps in the definition of a unified proof theoretical framework for logics equipped with a comparative plausibility operator.

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arXiv2022

Cyclic Proofs, Hypersequents, and Transitive Closure Logic

We propose a cut-free cyclic system for Transitive Closure Logic (TCL) based on a form of hypersequents, suitable for automated reasoning via proof search. We show that previously proposed sequent systems are cut-free incomplete for basic validities from Kleene Algebra (KA) and Propositional Dynamic Logic (PDL), over standard translations. On the other hand, our system faithfully simulates known cyclic systems for KA and PDL, thereby inheriting their completeness results. A peculiarity of our system is its richer correctness criterion, exhibiting 'alternating traces' and necessitating a more intricate soundness argument than for traditional cyclic proofs.

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arXiv2020

Uniform labelled calculi for preferential conditional logics based on neighbourhood semantics

The preferential conditional logic PCL, introduced by Burgess, and its extensions are studied. First, a natural semantics based on neighbourhood models, which generalise Lewis' sphere models for counterfactual logics, is proposed. Soundness and completeness of PCL and its extensions with respect to this class of models are proved directly. Labelled sequent calculi for all logics of the family are then introduced. The calculi are modular and have standard proof-theoretical properties, the most important of which is admissibility of cut, that entails a syntactic proof of completeness of the calculi. By adopting a general strategy, root-first proof search terminates, thereby providing a decision procedure for PCL and its extensions. Finally, the semantic completeness of the calculi is established: from a finite branch in a failed proof attempt it is possible to extract a finite countermodel of the root sequent. The latter result gives a constructive proof of the finite model property of all the logics considered.

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