Related papers: A Deep-Inference Sequent Calculus for Basic Propos…
This paper introduces and studies the sequential composition and decomposition of propositional logic programs. We show that acyclic programs can be decomposed into single-rule programs and provide a general decomposition result for…
Je\v{r}\'abek showed that cuts in classical propositional logic proofs in deep inference can be eliminated in quasipolynomial time. The proof is indirect and it relies on a result of Atserias, Galesi and Pudl\'ak about monotone sequent…
Lorenzen's ``Algebraische und logistische Untersuchungen \"uber freie Verb\"ande'' appeared in 1951 in The journal of symbolic logic. These ``Investigations'' have immediately been recognised as a landmark in the history of infinitary proof…
Gentzen designed his natural deduction proof system to ``come as close as possible to actual reasoning.'' Indeed, natural deduction proofs closely resemble the static structure of logical reasoning in mathematical arguments. However,…
We investigate non-wellfounded proof systems based on parsimonious logic, a weaker variant of linear logic where the exponential modality ! is interpreted as a constructor for streams over finite data. Logical consistency is maintained at a…
We present a proof system for the provability logic GLP in the formalism of nested sequents and prove the cut elimination theorem for it. As an application, we obtain the reduction of GLP to its important fragment called J syntactically.
Strict-Tolerant Logic (ST) underpins naive theories of truth and vagueness (respectively including a fully disquotational truth predicate and an unrestricted tolerance principle) without jettisoning any classically valid laws. The classical…
In this paper we study the deductive properties of a family of 3-valued paraconsistent logics. We define a notion of standard sequent calculus and prove that there is no sound and complete standard sequent calculus for these logics.…
We present a modification of the superposition calculus that is meant to generate consequences of sets of first-order axioms. This approach is proven to be sound and deductive-complete in the presence of redundancy elimination rules,…
We consider a simple modal logic whose non-modal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
Public announcement logic(PAL) is an extension of epistemic logic (EL) with some reduction axioms. In this paper, we propose a cut-free labelled sequent calculus for PAL, which is an extension of that for EL with sequent rules adapted from…
We introduce a new Gentzen-style framework of grafted hypersequents that combines the formalism of nested sequents with that of hypersequents. To illustrate the potential of the framework, we present novel calculi for the modal logics…
Basic proof-search tactics in logic and type theory can be seen as the root-first applications of rules in an appropriate sequent calculus, preferably without the redundancies generated by permutation of rules. This paper addresses the…
In this paper, we introduce a novel team semantics of LTL inspired by inquisitive logic. The main features of the resulting logic, we call InqLTL, are the intuitionistic interpretation of implication and the Boolean semantics of…
This paper defines a new proof- and category-theoretic framework for classical linear logic that separates reasoning into one linear regime and two persistent regimes corresponding to ! and ?. The resulting linear/producer/consumer (LPC)…
In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are…
The {\em tetravalent modal logic} ($\cal TML$) is one of the two logics defined by Font and Rius (\cite{FR2}) (the other is the {\em normal tetravalent modal logic} ${\cal TML}^N$) in connection with Monteiro's tetravalent modal algebras.…
Development of a contraction-free BI sequent calculus, be it in the sense of G3i or G4i, has not been successful in literature. We address the open problem by presenting such a sequent system. In fact our calculus involves no structural…
We consider G\"odel temporal logic ($\sf GTL$), a variant of linear temporal logic based on G\"odel--Dummett propositional logic. In recent work, we have shown this logic to enjoy natural semantics both as a fuzzy logic and as a…