Edwin Mares

The sentential logic S extends classical logic by an implication-like connective. The logic was first presented by Chellas as the smallest system modelled by contraining the Stalnaker-Lewis semantics for counterfactual conditionals such that the conditional is effectively evaluated as in the ternary relations semantics for relevant logics. The resulting logic occupies a key position among modal and substructural logics. We prove completeness results and study conditions for proceeding from one family of logics to another

In "General Information in Relevant Logic" (Synthese 167, 2009), the semantics for relevant logic is interpreted in terms of objective information. Objective information is potential data that is available in an environment. This paper explores the notion of objective information further. The concept of availability in an environment is developed and used as a foundation for the semantics, in particular, as a basis for the understanding of the information that is expressed by relevant implication. It is also used to understand the nature of misinformation. A form of relevant logic—called "LOI" for "logic of objective information"—is presented and the relationship between the justification of its proof theory and the semantics is discussed. This relationship is rather reciprocal. Intuitive features of the logic are used to interpret and justify aspects of the model theory and intuitive aspects of the model theory are used to interpret and justify features of the logic. Information conditions are presented for the connectives and the way that they fit into the theory of information is discussed

This paper sets out three programmes that attempt to use relevant logic as the basis for a philosophy of mathematics. Although these three programmes do not exhaust the possible approaches to mathematics through relevant logic, they are fairly representative of the current state of the field. The three programmes are compared and their relative strengths and weaknesses set out. At the end of the paper I examine the consequences of adopting each programme for the realist debate about mathematical objects.

This paper sets out a philosophical interpretation of the model theory of Mares and Goldblatt (The Journal of Symbolic Logic 71, 2006). This interpretation distinguishes between truth conditions and information conditions. Whereas the usual Tarskian truth condition holds for universally quantified statements, their information condition is quite different. The information condition utilizes general propositions . The present paper gives a philosophical explanation of general propositions and argues that these are needed to give an adequate theory of general information.

This chapter distinguishes semantic and metaphysical problems facing Molinism. In the past thirty years, there has been a fair amount of uncertainty and confusion in the literature over the relationship between Molinist counterfactuals of freedom and the standard possible‐worlds semantics for counterfactuals. The authors show that Molinism is compatible with the standard semantics. They argue that two semantic arguments against Molinism‐the Might Argument and the Tie Argument—fail. Friends and foes of Molinism have typically failed to appreciate that the similarity relation that is appropriate to evaluate (both ‘would’ and ‘might’) counterfactuals is (unless they express strict conditionals) context-dependent. There is no one similarity relation that suits all contexts.

The article ‘A Note on Strict Implication’ was submitted for publication by C.I. Lewis and C.H. Langford but withdrawn in proof. The paper is, according to notes and letters by both Lewis and Langford, largely by Lewis. It constitutes an early attempt by Lewis to give meanings for the modal connectives using abstract objects. To be necessary, for example, is for a statement to have the same intension as a truth-functional tautology. This theory prefigures the view of Lewis's 1946 book, Analysis of Knowledge and Valuation. This introduction to the article looks at the historical background of the piece in addition to its argument and examines why it was withdrawn.