In this paper, which is part of the Zsyntax project outlined in Boniolo et al. (2010) [2], we provide a proof-theoretical setting for the study of context-sensitive interactions by means of a non-monotonic conjunction operator. The resulting system is a non-associative variant of MLLpol (the multiplicative polarised fragment of Linear Logic) in which the monotonicity of interactions, depending on the context, is governed by specific devices called control sets. Following the spirit of Linear Logic, the ordinary sequent calculus presentation is also framed into a theory of proof-nets and the set of sequential proofs is shown to be sound and complete with respect to the class of corresponding proof-nets. Some possible biochemical applications are also discussed

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The aim of this paper is to argue that logic can play an important role in the “toolbox” of molecular biology. We show how biochemical pathways, i.e., transitions from a molecular aggregate to another molecular aggregate, can be viewed as deductive processes. In particular, our logical approach to molecular biology — developed in the form of a natural deduction system — is centered on the notion of Curry-Howard isomorphism, a cornerstone in nineteenth-century proof-theory

Some real life processes, including molecular ones, are context-sensitive, in the sense that their outcome depends on side conditions that are most of the times difficult, or impossible, to express fully in advance. In this paper, we survey and discuss a logical account of context-sensitiveness in molecular processes, based on a kind of non-classical logic. This account also allows us to revisit the relationship between logic and philosophy of science (and philosophy of biology, in particular).

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