Constant Domain Quantified Modal Logics Without Boolean Negation

his paper provides a sound and complete axiomatisation for constant domain modal logics without Boolean negation. This is a simpler case of the difficult problem of providing a sound and complete axiomatisation for constant-domain quantified relevant logics, which can be seen as a kind of modal logic with a two-place modal operator, the relevant conditional. The completeness proof is adapted from a proof for classical modal predicate logic (I follow James Garson’s 1984 presentation of the completeness proof quite closely), but with an important twist, to do with the absence of Boolean negation

Editorial

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Models for Substructural Arithmetics

This paper explores models for arithmetic in substructural logics. In the existing literature on substructural arithmetic, frame semantics for substructural logics are absent. We will start to fill in the picture in this paper by examining frame semantics for the substructural logics C (linear logic plus distribution), R (relevant logic) and CK (C plus weakening). The eventual goal is to find negation complete models for arithmetic in R

Structural rules in natural deduction with alternatives

Natural deduction with alternatives extends Gentzen–Prawitz-style natural deduction with a single structural addition: negatively signed assumptions, called alternatives. It is a mildly bilateralist, single-conclusion natural deduction proofsystem in which the connective rules are unmodified from the usual Prawitz introduction and elimination rules — the extension is purely structural. This framework is general: it can be used for (1) classical logic, (2) relevant logic without distribution, (3) affine logic, and (4) linear logic, keeping the connective rules fixed, and varying purely structural rules. The key result of this paper is that the two principles that introduce kindsofirrelevanceto natural deduction proofs: (a) the rule of explosion (from acontradiction, anything follows); and (b) the structural rule of vacuous discharge;are shown to be two sides of a single coin, in the same way that they correspond tothe structural rule of weakening in the sequent calculus. The paper also includes a discussion of assumption classes, and how they can play a role in treating additive connectives in substructural natural deduction.Publisher PDFPeer reviewe

Fixed-Point Models for Theories of Properties and Classes

There is a vibrant (but minority) community among philosophical logicians seeking to resolve the paradoxes of classes, properties and truth by way of adopting some non-classical logic in which trivialising paradoxical arguments are not valid. There is also a long tradition in theoretical computer science|going back to Dana Scott's fixed point model construction for the untyped lambda-calculus of models allowing for fixed points. In this paper, I will bring these traditions closer together, to show how these model constructions can shed light on what we could hope for in a non-trivial model of a theory for classes, properties or truth featuring fixed points

Models for Substructural Arithmetics

This paper explores models for arithmetic in substructural logics. In the existing literature on substructural arithmetic, frame semantics for substructural logics are absent. We will start to fill in the picture in this paper by examining frame semantics for the substructural logics C (linear logic plus distribution), R (relevant logic) and CK (C plus weakening). The eventual goal is to find negation complete models for arithmetic in R

Exploring the experience of Year 10 South Korean students’ English language learning in immersive virtual reality.

A prescribed English language textbook often directs classroom teaching practices in secondary school classes in EFL contexts, such as in South Korea. The textbook is often accompanied by multimedia resources which are delivered to students as input at a regulated pace with limited opportunities for communicative interaction or spoken output. Such opportunities are further limited in the community outside of the English classroom. Immersive virtual reality (i-VR) has the potential to situate learners in a real-world context for authentic application of textbook language learning. English teachers in the formal classroom focus on linguistic competence development within time constraints by teaching new vocabulary and grammatical items in decontextualised forms. By comparison, i-VR environments focus on learning to construct meaning in communicative events in contextualised, real-world settings based on students’ existing linguistic knowledge and ability. In a small-scale pilot study, two teachers of Year 10 English classes in Seoul implemented four i-VR language learning modules in their classes: one as a self-directed learning experience that extended beyond formal classroom learning, and the other as a teacher-facilitated learning experience within the formal classroom. Both teachers were interviewed after the two-week implementation to seek their views on their perceptions of the value of such i-VR learning for their students. Beyond the motivational and entertainment value, the teachers viewed the i-VR experience as capable of incorporating pedagogical structures using the embedded multimodal resources that is not possible in other immersive forms of language learning. Moreover, the teachers believed that incorporation of authentic conversations and interactional opportunities could further enhance the learning potential