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The entire development of modern logic is characterized by various forms of confrontation of what has come to be called proof theory with what has earned the label of model theory. For a long time the widely accepted view was that while model theory captures directly what logical formalisms are about, proof theory is merely our technical means of getting some incomplete grip on this; but in recent decades the situation has altered. Not only did proof theory expand into new realms, generalizing the concept of proof in various directions; many philosophers also realized that meaning may be seen as primarily consisting in certain rules rather than in language-world links. However, the possibility of construing meaning as an inferential role is often seen as essentially compromised by the limits of proof-theoretical means. The aim of this paper is to sort out the cluster of problems besetting logical inferentialism by disentangling and clarifying one of them, namely determining the power of various inferential frameworks as measured by that of explicitly semantic ones. [ABSTRACT FROM AUTHOR]

This paper asks why information should ever be expressed vaguely, re-assessing some previously proposed answers to this question and suggesting some new ones. Particular attention is paid to the benefits that vague expressions can have in situations where agreement over the meaning of an expression cannot be taken for granted. A distinction between two different versions of the above-mentioned question is advocated. The first asks why human languages contain vague expressions, the second question asks when and why a speaker should choose a vague expression when communicating with a hearer. While the former question is purely theoretical, the latter has practical implications for the computational generation of utterances in Natural Language Generation (NLG). [ABSTRACT FROM AUTHOR]

In a recent paper Johan van Benthem reviews earlier work done by himself and colleagues on ‘natural logic’. His paper makes a number of challenging comments on the relationships between traditional logic, modern logic and natural logic. I respond to his challenge, by drawing what I think are the most significant lines dividing traditional logic from modern. The leading difference is in the way logic is expected to be used for checking arguments. For traditionals the checking is local, i.e. separately for each inference step. Between inference steps, several kinds of paraphrasing are allowed. Today we formalise globally: we choose a symbolisation that works for the entire argument, and thus we eliminate intuitive steps and changes of viewpoint during the argument. Frege and Peano recast the logical rules so as to make this possible. I comment also on the traditional assumption that logical processing takes place at the top syntactic level, and I question Johan’s view that natural logic is ‘natural’. [ABSTRACT FROM AUTHOR]

We compare fork arrow logic, an extension of arrow logic, and its natural first-order counterpart (the correspondence language) and show that both have the same expressive power. Arrow logic is a modal logic for reasoning about arrow structures, its expressive power is limited to a bounded fragment of first-order logic. Fork arrow logic is obtained by adding to arrow logic the fork modality (related to parallelism and synchronization). As a result, fork arrow logic attains the expressive power of its first-order correspondence language, so both can express the same input–output behavior of processes. [ABSTRACT FROM AUTHOR]

Establishes formal connections between deontic and nonmonotonic logic. Ways by which nonmonotonic reasoning might help illuminate deontic ideas. Account of obligation; Default logic; Introduction; Oughts and imperatives; Default logic; Imperatives as defaults; Conditional oughts; Problems with conditional oughts; Conclusion.

Presents an argument against a global supervenience of all mental properties on physical state of affairs. Restriction of possible world semantics according to David Kaplan; O-interpretations; Global supervenience.

Presents a study of logics that have the MacIntosh rule formulated by J.J. MacIntosh. Background on modal logics; Features of the MacIntosh rule; Definition of MacIntosh logic; Logics with the rule and their common theorems; Smallest MacIntosh logic; Genuine Macintosh logics; Applying MacIntosh rule in philosophical reasoning; MacIntosh territory.