Related papers: On the Correspondence between Display Postulates a…
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 formulas of the first order language of enriched formal contexts,…
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 language which is interpreted on the canonical extensions of…
We introduce proper display calculi for basic monotonic modal logic, the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…
We present some hypersequent calculi for all systems of the classical cube and their extensions with axioms $T$, $P$, $D$, and, for every $n\geq 1$, rule $RD^+_n$. The calculi are internal as they only employ the language of the logic, plus…
Nakano's "later" modality, inspired by G\"{o}del-L\"{o}b provability logic, has been applied in type systems and program logics to capture guarded recursion. Birkedal et al modelled this modality via the internal logic of the topos of…
Warning: This paper contains a mistake, rendering the proof of the main theorem invalid. The logic of Bunched Implications (BI) combines both additive and multiplicative connectives, which include two primitive intuitionistic implications.…
An inductive inference system for proving validity of formulas in the initial algebra $T_{\mathcal{E}}$ of an order-sorted equational theory $\mathcal{E}$ is presented. It has 20 inference rules, but only 9 of them require user interaction;…
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 tableaux calculi, a refutation approach to display calculi…
Extending and generalizing the approach of 2-sequents (Masini, 1992), we present sequent calculi for the classical modal logics in the K, D, T, S4 spectrum. The systems are presented in a uniform way-different logics are obtained by tuning…
We introduce the first cut-free nested sequent systems for first-order modal logics that admit increasing, decreasing, constant, and empty domains along with so-called general path conditions and seriality. We obtain such systems by means…
On the ground of a general theorem concerning the admissibility of the structural rules in sequent calculi with additional atomic rules, we develop a proof theoretic analysis for several extensions of the ${\bf G3[mic]}$ sequent calculi…
We introduce a proper display calculus for first-order logic, of which we prove soundness, completeness, conservativity, subformula property and cut elimination via a Belnap-style metatheorem. All inference rules are closed under uniform…
We introduce proper display calculi for intuitionistic, bi-intuitionistic and classical linear logics with exponentials, which are sound, complete, conservative, and enjoy cut-elimination and subformula property. Based on the same design,…
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…
In this paper, we introduce a general family of sequent-style calculi over the modal language and its fragments to capture the essence of all constructively acceptable systems. Calling these calculi \emph{constructive}, we show that any…
Modelling semantic similarity plays a fundamental role in lexical semantic applications. A natural way of calculating semantic similarity is to access handcrafted semantic networks, but similarity prediction can also be anticipated in a…
Inference systems are a widespread framework used to define possibly recursive predicates by means of inference rules. They allow both inductive and coinductive interpretations that are fairly well-studied. In this paper, we consider a…
Specification languages are essential in deductive program verification, but they are usually based on first-order logic, hence less expressive than the programs they specify. Recently, trace specification logics with fixed points that are…
In this paper, we introduce two focussed sequent calculi, LKp(T) and LK+(T), that are based on Miller-Liang's LKF system for polarised classical logic. The novelty is that those sequent calculi integrate the possibility to call a decision…