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Refutation calculi for lattice-based logics: from display to tableaux
Andrea De Domenico, Giuseppe Greco, Alessandra Palmigiano +2
Refutation calculi are formal systems developed to derive the invalid formulas of a given logic. While the notion of refutation calculi has played a key role in the development of…
Inception Display Calculi
Andrea De Domenico, Giuseppe Greco, Alessandra Palmigiano
Display calculi were introduced by Nuel Belnap in `Display logic' (1982) as a natural extension of Gentzen's sequent calculi, as a uniform and modular framework capable of encompas…
Modular constructive Lyndon interpolation for nondistributive logics
Andrea De Domenico, Giuseppe Greco, Alessandra Palmigiano +1
We establish the Lyndon interpolation property for basic lattice expansion logics (LE-logics) in arbitrary signatures using display calculi. Our approach is constructive, yielding…
Obligations and permissions, algebraically
Andrea De Domenico, Ali Farjami, Krishna Manoorkar +3
We further develop the algebraic approach to input/output logic initiated in \cite{wollic22}, where subordination algebras and a family of their generalizations were proposed as a…
Obligations and permissions on selfextensional logics
Andrea De Domenico, Ali Farjami, Krishna Manoorkar +3
We further develop the abstract algebraic logic approach to input/output logic initiated in \cite{wollic22}, where the family of selfextensional logics was proposed as a general ba…
Labelled calculi for the logics of rough concepts
Ineke van der Berg, Andrea De Domenico, Giuseppe Greco +3
We introduce sound and complete labelled sequent calculi for the basic normal non-distributive modal logic L and some of its axiomatic extensions, where the labels are atomic formu…
Labelled calculi for lattice-based modal logics
Ineke van der Berg, Andrea De Domenico, Giuseppe Greco +3
We introduce labelled sequent calculi for the basic normal non-distributive modal logic L and 31 of its axiomatic extensions, where the labels are atomic formulas of a first order…
Non-distributive description logic
Ineke van der Berg, Andrea De Domenico, Giuseppe Greco +3
We define LE-ALC, a generalization of the description logic ALC based on the propositional logic of general (i.e. not necessarily distributive) lattices, and semantically interpret…
Algorithmic correspondence and analytic rules
Andrea De Domenico, Giuseppe Greco, Alessandra Palmigiano
We introduce the algorithm MASSA which takes classical modal formulas in input, and, when successful, effectively generates: (a) (analytic) geometric rules of the labelled calculus…