The seven virtues of simple type theory

Farmer, William M.

doi:10.1016/j.jal.2007.11.001

Cited by 53 publications

(51 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To justify this claim, we now examine the two settings from several points of view. For a highly readable account of this topic that is more detailed than we have space for here, we strongly recommend [19].…”

Section: Discussionmentioning

confidence: 99%

“…Mathematical concepts are easy to express directly in higher-order logic because, amongst other things, the logic allows quantification over predicates and functions. This is illustrated by the direct modelling of probabilistic concepts such as densities and operations on them in higher-order theories; other good examples are given in [19]. In contrast, first-order logic only allows one to model many mathematical concepts indirectly and requires the introduction of (semantically complicated) set theory to give a satisfactory foundation for mathematics.…”

Section: Discussionmentioning

confidence: 99%

“…Next there is the TV guide that maps occurrences to programs. (20,7,2007), (11,30), Win)) (21,7,2007), (19,30), ABC )) (21,7,2007), (20,30), ABC ))…”

Section: Examplementioning

confidence: 99%

See 2 more Smart Citations

Probabilistic modelling, inference and learning using logical theories

Lloyd

Uther

2008

Ann Math Artif Intell

View full text Add to dashboard Cite

This paper provides a study of probabilistic modelling, inference and learning in a logic-based setting. We show how probability densities, being functions, can be represented and reasoned with naturally and directly in higher-order logic, an expressive formalism not unlike the (informal) everyday language of mathematics. We give efficient inference algorithms and illustrate the general approach with a diverse collection of applications. Some learning issues are also considered.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Probabilistic modelling, inference and learning using logical theories

Lloyd

Uther

2008

Ann Math Artif Intell

View full text Add to dashboard Cite

show abstract

“…The concept of infinity (Biza, Nardia, & González-Martín, 2009;Mamolo & Zazkis, 2008), the Riemann integral (Thomson, 2007(Thomson, , 2010, and the completeness property of the set of real numbers (Bergé, 2008(Bergé, , 2010 were repeated topics. The remaining papers in this category addressed issues at the interface of mathematics, computer science and engineering (Terlaky, 2001;Tremblay, 2000;Farmer, 2008).…”

Section: Subject-specific Contentmentioning

confidence: 99%

Enhancing Assessment in Teacher Education Courses

Roscoe

2013

cjsotl-rcacea

View full text Add to dashboard Cite

Several faculty members including the author were involved in exploring the implementation and effectiveness of research-based assessment strategies in their undergraduate teacher education courses at a Canadian university. The paper describes the process and the results of their ongoing improvement efforts and implications for teacher education and higher education in general. After attending several assessment workshops lead by the author, 12 faculty members implemented new assessment strategies in their own courses to enhance student learning. As the 12 faculty members reflected on their efforts to enhance assessment, a number of themes emerged. These included assessment as authentic performance, establishing clear learning targets, collaboration and community, and integrated assessment and instruction. Our results support the claim that current ideas about K-12 assessment are applicable to post-secondary education and can improve student learning outcomes. Developing balanced and integrated assessment systems is perhaps the most significant innovation we engaged in and we conclude that it has the potential to fundamentally change what occurs in university classrooms. Plusieurs professeurs, y compris l’auteur, ont exploré la mise en oeuvre et l’efficacité de stratégies d’évaluation basées sur la recherche dans le cadre de leurs cours de formation pour les enseignants. L’article décrit le processus et les résultats de leurs efforts pour améliorer la formation des enseignants et plus généralement l’enseignement, ainsi que les implications de cette approche. Après avoir participé à plusieurs ateliers sur l’évaluation dirigés par l’auteur, 12 professeurs ont mis en oeuvre de nouvelles stratégies d’évaluation dans leurs propres cours pour améliorer l’apprentissage des étudiants. Quand les 12 professeurs ont réfléchi sur leurs efforts pour améliorer l’évaluation, un certain nombre de thèmes sont apparus, entre autres : l’évaluation en tant que performance authentique, l’établissement d’objectifs d’apprentissage clairs, la collaboration et la communauté, l’intégration de l’évaluation et de l’instruction. Nos résultats étayent l’affirmation selon laquelle les théories actuelles sur l’évaluation dans les écoles (K-12) sont applicables en enseignement post-secondaire et peuvent améliorer l’apprentissage des étudiants. Le développement de systèmes d’évaluation équilibrés et intégrés est peut-être l’innovation la plus importante dans laquelle nous nous engageons et nous en concluons que cette pratique a le potentiel de changer radicalement ce qui se passe dans les salles de classe des universités.

show abstract

“…Following [20,21], we formalize modal logic as a fragment of simple type theory (see [9] to get started). This way we can make use of a rich syntactic and semantic framework and modal logic does not appear as an isolated formal system.…”

Section: Modal Logic In Simple Type Theorymentioning

confidence: 99%