Since the early days of artificial intelligence (AI), many logics have been explored as tools for knowledge representation and reasoning. In the spirit of the Crossley Festscrift and recognizing John Crossley’s diverse interests and his legacy in both mathematical logic and computer science, I discuss examples from my own research that sit in the overlap of logic and AI, with a focus on supporting human–AI interactions.

A sentence like every circle is blue might be understood in terms of individuals and their properties or in terms of a relation between groups. Relatedly, theorists can specify the contents of universally quantified sentences in first-order or second-order terms. We offer new evidence that this logical first-order vs. second-order distinction corresponds to a psychologically robust individual vs. group distinction that has behavioral repercussions. Participants were shown displays of dots and asked to evaluate sentences with each, every, or all combined (...) with a predicate. We find that participants are better at estimating how many things the predicate applied to after evaluating sentences in which universal quantification is indicated with every or all, as opposed to each. We argue that every and all are understood in second-order terms that encourage group representation, while each is understood in first-order terms that encourage individual representation. Since the sentences that participants evaluate are truth-conditionally equivalent, our results also bear on questions concerning how meanings are related to truth-conditions. (shrink)

The objectives of this paper are twofold. The first is to present a differentiation between two kinds of deferred uses of indexicals: those in which indexical utterances express singular propositions (I term them deferred reference proper) and those where they express general propositions (called descriptive uses of indexicals). The second objective is the analysis of the descriptive uses of indexicals. In contrast to Nunberg, who treats descriptive uses as a special case of deferred reference in which a property contributes to (...) the proposition expressed, I argue that examples in which a general proposition is indeed expressed by an indexical cannot be treated by assuming that the property is a deferred referent of the pronoun. I propose an analysis of descriptive uses of indexicals by means of a pragmatic mechanism of ‘descriptive anaphora’, which attempts to explain the special kind of contribution of the property retrieved from the context to the proposition that is characteristic of the descriptive interpretation. (shrink)

In Pietroski ( 2018 ) a simple representation language called SMPL is introduced, construed as a hypothesis about core conceptual structure. The present work is a study of this system from a logical perspective. In addition to establishing a completeness result and a complexity characterization for reasoning in the system, we also pinpoint its expressive limits, in particular showing that the fourth corner in the square of opposition (“ Some_not ”) eludes expression. We then study a seemingly small extension, called (...) SMPL +, which allows for a minimal predicate-binding operator. Perhaps surprisingly, the resulting system is shown to encode precisely the concepts expressible in first-order logic. However, unlike the latter class, the class of SMPL + expressions admits a simple procedural (context-free) characterization. Our contribution brings together research strands in logic—including natural logic, modal logic, description logic, and hybrid logic—with recent advances in semantics and philosophy of language. (shrink)

The impossibility results of Bovens and Hartmann (2003, Bayesian epistemology. Oxford: Clarendon Press) and Olsson (2005, Against coherence: Truth, probability and justification. Oxford: Oxford University Press.) show that the link between coherence and probability is not as strong as some have supposed. This paper is an attempt to bring out a way in which coherence reasoning nevertheless can be justified, based on the idea that, even if it does not provide an infallible guide to probability, it can give us an (...) indication thereof. It is further shown that this actually is the case, for several of the coherence measures discussed in the literature so far. We also discuss how this affects the possibility to use coherence as a means of epistemic justification. (shrink)