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In Poggiolesi [. Grounding principles for implication. Synthese, 1–28], a definition of the notion of grounding in the background of a relevant framework has been introduced; this... 

Seemingly natural principles about the logic of ground generate cycles of ground; how can this be if ground is asymmetric? The goal of the theory of decycling is to find systematic and principled ways of getting rid of such cycles of ground. In this paper—drawing on graphtheoretic and topological ideas—I develop a general framework in which various theories of decycling can be compared. This allows us to improve on proposals made earlier by Fine and Litland. However, it turns out that (...) 

I outline and provide a solution to some paradoxes of ground. 

An oftdefended claim of a close relationship between Gentzen inference rules and the meaning of the connectives they introduce and eliminate has given rise to a whole domain called prooftheoretic semantics, see Schroeder Heister ; Prawitz. A branch of prooftheoretic semantics, mainly developed by Dosen ; Dosen and Petric, isolates in a precise mathematical manner formulas that have the same meaning. These isomorphic formulas are defined to be those that behave identically in inferences. The aim of this paper is to (...) 

This is part two of a twopart paper in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. In this part of the paper, we extend the base theory of the first part of the paper with hierarchically typed truthpredicates and principles about the interaction of partial ground and truth. We show that our theory is (...) 

Could φ’s partially grounding ψ itself be a partial ground for ψ? I show that it follows from commonly accepted principles in the logic of ground that this sometimes happens. It also follows from commonly accepted principles that this never happens. I show that this inconsistency turns on different principles than the puzzles of ground already discussed in the literature, and I propose a way of resolving the inconsistency. 

Most of the logics of grounding that have so far been proposed contain grounding axioms, or grounding rules, for the connectives of conjunction, disjunction and negation, but little attention has been dedicated to the implication connective. The present paper aims at repairing this situation by proposing adequate grounding principles for relevant implication. Because of the interaction between negation and implication, new grounding principles concerning negation will also arise. 