The Journal of Logic and Computation (OUP) has launched a new section devoted to Logic and Philosophy of Information edited by Luciano Floridi and Marcello D’Agostino. The editors welcome papers on the relationship between logic and information, including philosophical aspects, provided they have a mathematical/computational content.
From the editorial:
While the existence of a fundamental relationship between logic and information seems unquestionable, its precise nature has so far proved to be rather elusive and somewhat puzzling. The received view on this issue is epitomized by the traditional tenet that logical inference is ‘tautological’ (literally, repetitive and trivially true), namely that a valid inference is one in which the information carried by the conclusion is (in a sense variously specified) contained in the information carried by the (conjunction of the) premises. At the mid of the 20th century, Bar-Hillel and Carnap’s controversial theory of ‘semantic information’ provided what is, to date, the strongest theoretical justification for this tenet. However, as remarked by a number of authors who have made the history of logic, including Frege, Dummett and Hintikka, the received view clashes with the intuitive idea that deductive arguments are useful just because, by their means, we obtain information that we did not possess before. Moreover, it also clashes with two 20th-century milestones of the theory of computation: the undecidability of first-order logic and the NP-hardness of propositional logic. How can logic be informationally trivial and, yet, computationally hard? Can we obtain an informational characterization of logical consequence that is more in tune with our intuition and with the negative results on the computational complexity of logical reasoning? read more