Hamkins and Löwe proved that the modal logic of forcing is S4.2. In this paper, we consider its modal companion, the intermediate logic KC and relate it to the fatal Heyting algebra HZFC of forcing persistent sentences. This Heyting algebra is equationally generic for the class of fatal Heyting algebras. Motivated by these results, we further analyse the class of fatal Heyting algebras.

In 1990 Krivine (1990b) introduced the notion of storage operators. They are λ-terms which simulate call-by-value in the call-by-name strategy. Krivine (1990b) has shown that there is a very simple type in the AF2 type system for storage operators using Gődel translation from classical to intuitionistic logic. Parigot (1993a) and Krivine (1994) have shown that storage operators play an importan...

We describe a BDI (Belief, Desire, Intention) goal-oriented architecture for a conversational virtual companion embodied as a child’s Toy, designed to be both entertaining and capable of carrying out collaborative tasks. We argue that the goal-oriented approach supports both structured conversational activities (e.g., story-telling, collaborative games) as well as more “free-flowing” engaging d...

Older adults with strong social connections are at a reduced risk for health problems and mortality. We describe two field studies to inform the development of a virtual agent designed to provide long-term, continuous social support to isolated older adults. Findings include the topics that older adults would like to discuss with a companion agent, in addition to overall reactions to interactin...

This article examines the regulation of companion animal welfare during disasters, with some context provided by two recent major disaster events in Australia. Important general lessons for improved disaster management were identified in subsequent inquiries. However, the interests of companion animals continue to be inadequately addressed. This is because key assumptions underpinning disaster ...

We describe a BDI (Belief, Desire, Intention) approach and architecture for a conversational virtual companion embodied as a child’s Toy. Our aim is to support both structured conversation-based activities (e.g., story-telling, collaborative games) as well as more free-flowing, engaging dialogue with variation and some unpredictability. We argue that a goal-oriented approach to the agent’s conv...

We report our findings on the properties of Flagg and Friedman’s translation from Epistemic into Intuitionistic logic, which was proposed as the basis of a comprehensive proof method for the faithfulness of the Gödel translation. We focus on the propositional case and raise the issue of the admissibility of the translated necessitation rule. Then, we contribute to Flagg and Friedman’s program b...