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  • Sentential Logic by Tony Roy

    Sentential Logic

    Tony Roy


    Excerpted from the longer Roy, Symbolic Logic, including chapter 1 and just the first parts of chapters 2 - 7.

    From the preface: There is, I think, a gap between what many students learn in their first course in formal logic, and what they are expected to know for their second. While courses in mathematical logic with metalogical components often cast only the barest glance at mathematical induction or even the very idea of reasoning from definitions, a first course may also leave these untreated, and fail explicitly to lay down the definitions upon which the second course is based. The aim of this text is to integrate material from these courses and, in particular, to make serious mathematical logic accessible to students I teach. The first parts introduce classical symbolic logic as appropriate for beginning students; the last parts build to Gödel’s adequacy and incompleteness results. A distinctive feature of the last section is a complete development of Gödel’s second incompleteness theorem.

    Contents

    Front Matter

    I The Elements: Four Notions of Validity

    1 Logical Validity and Soundness

    2 Formal Languages

    3 Axiomatic Deduction

    4 Semantics

    5 Translation

    6 Natural Deduction

    II Transition: Reasoning About Logic

    7 Direct Semantic Reasoning

    Answers to Selected Exercises

    Bibliography

  • Symbolic Logic by Tony Roy

    Symbolic Logic

    Tony Roy


    From the preface: There is, I think, a gap between what many students learn in their first course in formal logic, and what they are expected to know for their second. While courses in mathematical logic with metalogical components often cast only the barest glance at mathematical induction or even the very idea of reasoning from definitions, a first course may also leave these untreated, and fail explicitly to lay down the definitions upon which the second course is based. The aim of this text is to integrate material from these courses and, in particular, to make serious mathematical logic accessible to students I teach. The first parts introduce classical symbolic logic as appropriate for beginning students; the last parts build to Gödel’s adequacy and incompleteness results. A distinctive feature of the last section is a complete development of Gödel’s second incompleteness theorem.

    Contents

    Front Matter

    I The Elements: Four Notions of Validity

    1 Logical Validity and Soundness

    2 Formal Languages

    3 Axiomatic Deduction

    4 Semantics

    5 Translation

    6 Natural Deduction

    II Transition: Reasoning About Logic

    7 Direct Semantic Reasoning

    8 Mathematical Induction

    III Classical Metalogic: Soundness and Adequacy

    9 Preliminary Results

    10 Main Results

    11 More Main Results

    IV Logic and Arithmetic: Incompleteness and Computability

    12 Recursive Functions and Q

    13 Gödel’s Theorems

    14 Logic and Computability

    Concluding Remarks

    Answers to Selected Exercises

    Bibliography

  • Restorative Practices Training Manual by John M. Winslade, Elizabeth Espinoza, Michelle Myers, and Henry Yzaguirre

    Restorative Practices Training Manual

    John M. Winslade, Elizabeth Espinoza, Michelle Myers, and Henry Yzaguirre

    This manual is designed to support the process of training school personnel in the San Bernardino City Unified School District to implement Restorative Practices into the schools in their district. What is outlined below are the following:

    • The need that the introduction of restorative practices is designed to respond to
    • The key ideas and assumptions that underlie restorative practices
    • The training and consultation process that aims to implement these ideas in the school district
    • An explanation of the specific practices that training will be offered in
    • A summary of what current research data says about the value of these approaches
    • A bibliography of readings that interested and key personnel can follow up and read more about.

 
 
 

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