Lecture7_Model_theory_expanded

Lecture7_Model_theor - Ling 726 Mathematical Linguistics Lecture 7 Model Theory(expanded 2 V Borschev and B Partee October 12-14 2004 p 1 Lecture 7

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Unformatted text preview: Ling 726: Mathematical Linguistics, Lecture 7 Model Theory (expanded 2) V. Borschev and B. Partee, October 12-14, 2004 p. 1 Lecture 7. Model theory. Consistency, independence, completeness, categoricity of axiom systems. Expanded with algebraic view. CONTENTS 1. Syntactic provability and semantic entailment.......................................................................................................... 1 1.1. Semantic entailment and validity. ...................................................................................................................... 2 1.2. Soundness and completeness of a logic.............................................................................................................. 2 2. Consistency, completeness, independence, and other notions. ................................................................................ 3 2.1. Some syntactic concepts..................................................................................................................................... 3 2.2. Some semantic concepts..................................................................................................................................... 4 2.3. Soundness and completeness again.................................................................................................................... 4 2.4. Independence...................................................................................................................................................... 5 3. An algebraic view on provability and on the notions discussed above ..................................................................... 5 3.1. Closure systems.................................................................................................................................................. 5 Examples............................................................................................................................................................... 5 Closure operator.................................................................................................................................................... 6 Examples............................................................................................................................................................... 6 3.2. Galois connection............................................................................................................................................... 6 Examples............................................................................................................................................................... 7 4. Morphisms for models; categoricity........................................................................................................................ 7 Homework 8.................................................................................................................................................................. 8 Homework 8....
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This note was uploaded on 02/22/2012 for the course LINGUIST 726 taught by Professor Partee during the Spring '07 term at UMass (Amherst).

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Lecture7_Model_theor - Ling 726 Mathematical Linguistics Lecture 7 Model Theory(expanded 2 V Borschev and B Partee October 12-14 2004 p 1 Lecture 7

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