Matching Items (5)

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Supplementing Traditional Symbolic Logic Instruction with Historical Background and Real-World Applications

Description

A thorough understanding of the key concepts of logic is critical for student success. Logic is often not explicitly taught as its own subject in modern curriculums, which results in

A thorough understanding of the key concepts of logic is critical for student success. Logic is often not explicitly taught as its own subject in modern curriculums, which results in misconceptions among students as to what comprises logical reasoning. In addition, current standardized testing schemes often promote teaching styles which emphasize students' abilities to memorize set problem-solving methods over their capacities to reason abstractly and creatively. These phenomena, in tandem with halting progress in United States education compared to other developed nations, suggest that implementing logic courses into public schools and universities can better prepare students for professional careers and beyond. In particular, logic is essential for mathematics students as they transition from calculation-based courses to theoretical, proof-based classes. Many students find this adjustment difficult, and existing university-level courses which emphasize the technical aspects of symbolic logic do not fully bridge the gap between these two different approaches to mathematics. As a step towards resolving this problem, this project proposes a logic course which integrates historical, technical, and interdisciplinary investigations to present logic as a robust and meaningful subject warranting independent study. This course is designed with mathematics students in mind, with particular stresses on different formulations of deductively valid proof schemes. Additionally, this class can either be taught before existing logic classes in an effort to gradually expose students to logic over an extended period of time, or it can replace current logic courses as a more holistic introduction to the subject. The first section of the course investigates historical developments in studies of argumentation and logic throughout different civilizations; specifically, the works of ancient China, ancient India, ancient Greece, medieval Europe, and modernity are investigated. Along the way, several important themes are highlighted within appropriate historical contexts; these are often presented in an ad hoc way in courses emphasizing technical features of symbolic logic. After the motivations for modern symbolic logic are established, the key technical features of symbolic logic are presented, including: logical connectives, truth tables, logical equivalence, derivations, predicates, and quantifiers. Potential obstacles in students' understandings of these ideas are anticipated, and resolution methods are proposed. Finally, examples of how ideas of symbolic logic are manifested in many modern disciplines are presented. In particular, key concepts in game theory, computer science, biology, grammar, and mathematics are reformulated in the context of symbolic logic. By combining the three perspectives of historical context, technical aspects, and practical applications of symbolic logic, this course will ideally make logic a more meaningful and accessible subject for students.

Contributors

Created

Date Created
  • 2018-05

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Logical generics and gay identity

Description

Gays identity is usually cast in generics--statements about an indeterminate number of members in a given category. Sometimes these generic statements often get built up into folk definitions, vague and

Gays identity is usually cast in generics--statements about an indeterminate number of members in a given category. Sometimes these generic statements often get built up into folk definitions, vague and imprecise ways to talk about objects. Other times generics get co-opted into authentic definitions, definitions that pick out a few traits and assert that real members of the class have these traits and members that do not are simply members by a technicality. I assess how we adopt these generic traits into our language and what are the ramifications of using generic traits as a social identity. I analyze the use of authentic definitions in Queer Theory, particularly Michael Warner's use of authentic traits to define a normative Queer identity. I do not just simply focus on what are the effects, but how these folk or authentic definitions gain currency and, furthermore, how can they be changed. I conclude with an analytic account of what it means to be gay and argue that such an account will undercut many of the problems associated with folk or authentic definitions about being gay.

Contributors

Agent

Created

Date Created
  • 2012

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Representing and Reasoning about Dynamic Multi-Agent Domains: An Action Language Approach

Description

Reasoning about actions forms the basis of many tasks such as prediction, planning, and diagnosis in a dynamic domain. Within the reasoning about actions community, a broad class of languages,

Reasoning about actions forms the basis of many tasks such as prediction, planning, and diagnosis in a dynamic domain. Within the reasoning about actions community, a broad class of languages, called action languages, has been developed together with a methodology for their use in representing and reasoning about dynamic domains. With a few notable exceptions, the focus of these efforts has largely centered around single-agent systems. Agents rarely operate in a vacuum however, and almost in parallel, substantial work has been done within the dynamic epistemic logic community towards understanding how the actions of an agent may effect not just his own knowledge and/or beliefs, but those of his fellow agents as well. What is less understood by both communities is how to represent and reason about both the direct and indirect effects of both ontic and epistemic actions within a multi-agent setting. This dissertation presents ongoing research towards a framework for representing and reasoning about dynamic multi-agent domains involving both classes of actions.

The contributions of this work are as follows: the formulation of a precise mathematical model of a dynamic multi-agent domain based on the notion of a transition diagram; the development of the multi-agent action languages mA+ and mAL based upon this model, as well as preliminary investigations of their properties and implementations via logic programming under the answer set semantics; precise formulations of the temporal projection, and planning problems within a multi-agent context; and an investigation of the application of the proposed approach to the representation of, and reasoning about, scenarios involving the modalities of knowledge and belief.

Contributors

Agent

Created

Date Created
  • 2018

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Issues in the Normativity of Logic and the Logic as Model View

Description

After surveying the literature on the normativity of logic, the paper answers that logic is normative for reasoning and rationality. The paper then goes on to discuss whether this

After surveying the literature on the normativity of logic, the paper answers that logic is normative for reasoning and rationality. The paper then goes on to discuss whether this constitutes a new problem in issues in normativity, and the paper affirms that it does. Finally, the paper concludes by explaining that the logic as model view can address this new problem.

Contributors

Agent

Created

Date Created
  • 2017

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Representing and reasoning about goals and policies of agents

Description

Goal specification is an important aspect of designing autonomous agents. A goal does not only refer to the set of states for the agent to reach. A goal also defines

Goal specification is an important aspect of designing autonomous agents. A goal does not only refer to the set of states for the agent to reach. A goal also defines restrictions on the paths the agent should follow. Temporal logics are widely used in goal specification. However, they lack the ability to represent goals in a non-deterministic domain, goals that change non-monotonically, and goals with preferences. This dissertation defines new goal specification languages by extending temporal logics to address these issues. First considered is the goal specification in non-deterministic domains, in which an agent following a policy leads to a set of paths. A logic is proposed to distinguish paths of the agent from all paths in the domain. In addition, to address the need of comparing policies for finding the best ones, a language capable of quantifying over policies is proposed. As policy structures of agents play an important role in goal specification, languages are also defined by considering different policy structures. Besides, after an agent is given an initial goal, the agent may change its expectations or the domain may change, thus goals that are previously specified may need to be further updated, revised, partially retracted, or even completely changed. Non-monotonic goal specification languages that can make these changes in an elaboration tolerant manner are needed. Two languages that rely on labeling sub-formulas and connecting multiple rules are developed to address non-monotonicity in goal specification. Also, agents may have preferential relations among sub-goals, and the preferential relations may change as agents achieve other sub-goals. By nesting a comparison operator with other temporal operators, a language with dynamic preferences is proposed. Various goals that cannot be expressed in other languages are expressed in the proposed languages. Finally, plans are given for some goals specified in the proposed languages.

Contributors

Agent

Created

Date Created
  • 2010