From Logic to Montague Grammar:
Class Handouts


Some Formal Preliminaries

Formal Preliminaries 1: Relations and Functions

Formal Preliminaries 2: Cardinalities, Infinities, and Proof by Induction



A Review of Propositional Logic and First Order Logic

Propositional Logic: Syntax and Natural Deduction

First Order (Predicate) Logic: Syntax and Natural Deduction

Propositional Logic: Formal Semantics and Valuations

First Order Logic: Formal Semantics and Models

Proving the Soundness and Completeness of PL: Some Highlights

Key Applications of Model Theoretic Semantics for FOL: Soundness, Completeness, etc.



Algebras and Semantics

An Algebraic Perspective on Propositional Logic

An Algebraic Perspective on the Syntax of First Order Logic (Without Quantification)

Montague's General Theory of Semantics



Montague's Theory of Translation

Laying the Groundwork

The Notion of a 'Translation Base'

Translation Bases and Interpretations



An Algebraic Approach to Quantification and Lambda Abstraction

Preliminaries

Fregean Interpretations
  • Computing with Logically Possible Partly Fregean Interpretations

    Applications to the Analysis of English



    The Proper Treatment of Quantification in Ordinary English

    First Steps Towards PTQ: New Presentation of Our System for Quantifiers

    PTQ: The Fragment of English

    Intensional Logic

    The Translation System, Part 1

    The Translation System, Part 2



    Presentations by Seminar Participants

    On the History (and a Bit of Post-History) of Montague's PTQ [Presentation by Barbara Partee]

    On Idioms and Compositionality [Presentation by Stefan Keine]

    A Variation and Extension of a Montague Fragment of English [Presentation by Yangsook Park]

    The Logical Analysis of Plurals and Mass Terms [Presentation by Jon Ander Mendia]