The subsystem S of Parry's AI [10] (obtained by omitting modus ponens for the material conditional) is axiomatized and shown to be strongly complete for a class of three valued Kripke style models. It is proved that S is weakly complete for the class of consistent models, and therefore that Ackermann's rule is admissible in S. It also happens that S is decidable and contains the Lewis system S4 on translation — though these results are not presented here. S is (...) arguably the most relevant relevant logic known at this time to be decidable. (shrink)

This book aids in the rehabilitation of the wrongfully deprecated work of William Parry, and is the only full-length investigation into Parry-type propositional logics. A central tenet of the monograph is that the sheer diversity of the contexts in which the mereological analogy emerges – its effervescence with respect to fields ranging from metaphysics to computer programming – provides compelling evidence that the study of logics of analytic implication can be instrumental in identifying connections between topics that would otherwise remain (...) hidden. More concretely, the book identifies and discusses a host of cases in which analytic implication can play an important role in revealing distinct problems to be facets of a larger, cross-disciplinary problem. It introduces an element of constancy and cohesion that has previously been absent in a regrettably fractured field, shoring up those who are sympathetic to the worth of mereological analogy. Moreover, it generates new interest in the field by illustrating a wide range of interesting features present in such logics – and highlighting these features to appeal to researchers in many fields. (shrink)

I present a formal theory of the logic and aboutness of imagination. Aboutness is understood as the relation between meaningful items and what they concern, as per Yablo and Fine’s works on the notion. Imagination is understood as per Chalmers’ positive conceivability: the intentional state of a subject who conceives that p by imagining a situation—a configuration of objects and properties—verifying p. So far aboutness theory has been developed mainly for linguistic representation, but it is natural to extend it to (...) intentional states. The proposed framework combines a modal semantics with a mereology of contents: imagination operators are understood as variably strict quantifiers over worlds with a content-preservation constraint. (shrink)

I present a possible worlds semantics for a hyperintensional belief revision operator, which reduces the logical idealization of cognitive agents affecting similar operators in doxastic and epistemic logics, as well as in standard AGM belief revision theory. (Revised) belief states are not closed under classical logical consequence; revising by inconsistent information does not perforce lead to trivialization; and revision can be subject to ‘framing effects’: logically or necessarily equivalent contents can lead to different revisions. Such results are obtained without resorting (...) to non-classical logics, or to non-normal or impossible worlds semantics. The framework combines, instead, a standard semantics for propositional S5 with a simple mereology of contents. (shrink)

I discuss Yablo’s approach to truthmaker semantics and compare it with my own, with special focus on the idea of a proposition being true of or being restricted to some subject-matter, the idea of propositional containment, and the development of an ‘incremental’ semantics for the conditional. I conclude with some remarks on the relationship between truth-maker approach and the standard possible worlds approach to semantics.

We present a formal semantics for epistemic logic, capturing the notion of knowability relative to information (KRI). Like Dretske, we move from the platitude that what an agent can know depends on her (empirical) information. We treat operators of the form K_AB (‘B is knowable on the basis of information A’) as variably strict quantifiers over worlds with a topic- or aboutness- preservation constraint. Variable strictness models the non-monotonicity of knowledge acquisition while allowing knowledge to be intrinsically stable. Aboutness-preservation models (...) the topic-sensitivity of information, allowing us to invalidate controversial forms of epistemic closure while validating less controversial ones. Thus, unlike the standard modal framework for epistemic logic, KRI accommodates plausible approaches to the Kripke-Harman dogmatism paradox, which bear on non-monotonicity, or on topic-sensitivity. KRI also strikes a better balance between agent idealization and a non-trivial logic of knowledge ascriptions. (shrink)

Our topic is the theory of topics. My goal is to clarify and evaluate three competing traditions: what I call the way-based approach, the atom-based approach, and the subject-predicate approach. I develop criteria for adequacy using robust linguistic intuitions that feature prominently in the literature. Then I evaluate the extent to which various existing theories satisfy these constraints. I conclude that recent theories due to Parry, Perry, Lewis, and Yablo do not meet the constraints in total. I then introduce the (...) issue-based theory—a novel and natural entry in the atom-based tradition that meets our constraints. In a coda, I categorize a recent theory from Fine as atom-based, and contrast it to the issue-based theory, concluding that they are evenly matched, relative to our main criteria of adequacy. I offer tentative reasons to nevertheless favour the issue-based theory. (shrink)

We examine the relationship between the logics of nonsense of Bochvar and Halldén and the containment logics in the neighborhood of William Parry’s A I. We detail two strategies for manufacturing containment logics from nonsense logics—taking either connexive and paraconsistent fragments of such systems—and show how systems determined by these techniques have appeared as Frederick Johnson’s R C and Carlos Oller’s A L. In particular, we prove that Johnson’s system is precisely the intersection of Bochvar’s B 3 and Graham Priest’s (...) non-symmetrized connexive logic and that Oller’s system lies just beneath the intersection of B 3 and Priest’s paraconsistent L P. We conclude by examining Oller’s system in more depth, giving it a characterization in terms of L P and showing that it plays the same role to Harry Deutsch’s paraconsistent containment logic S that Aleksandr Zinov'ev’s S 1 plays with respect to A I. (shrink)

A modified filtrations argument is used to prove that the relevant logic S of [2] is decidable.