Searching for quantifiers : 14 results found | RSS Feed for this search

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18.100A Introduction to Analysis (MIT) 18.100A Introduction to Analysis (MIT)

Description

Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the pla Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the pla

Subjects

mathematical analysis | mathematical analysis | estimations | estimations | limit of a sequence | limit of a sequence | limit theorems | limit theorems | subsequences | subsequences | cluster points | cluster points | infinite series | infinite series | power series | power series | local and global properties | local and global properties | continuity | continuity | intermediate-value theorem | intermediate-value theorem | convexity | convexity | integrability | integrability | Riemann integral | Riemann integral | calculus | calculus | convergence | convergence | Gamma function | Gamma function | Stirling | Stirling | quantifiers and negation | quantifiers and negation | Leibniz | Leibniz | Fubini | Fubini | improper integrals | improper integrals | Lebesgue integral | Lebesgue integral | mathematical proofs | mathematical proofs | differentiation | differentiation | integration | integration

License

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24.921 Special Topics in Linguistics: Genericity (MIT) 24.921 Special Topics in Linguistics: Genericity (MIT)

Description

This course will investigate the semantics of generic sentences, i.e., sentences that are used to talk about habits, tendencies, dispositions, or kinds. For instance: Dogs are good pets. The giant panda is an endangered species. A soccer player makes lots of money. Mary smokes after dinner. This machine crushes oranges. This is a half-semester course. This course will investigate the semantics of generic sentences, i.e., sentences that are used to talk about habits, tendencies, dispositions, or kinds. For instance: Dogs are good pets. The giant panda is an endangered species. A soccer player makes lots of money. Mary smokes after dinner. This machine crushes oranges. This is a half-semester course.

Subjects

semantics of generic sentences | semantics of generic sentences | modality | modality | adverbial quantifiers | adverbial quantifiers | semantics of aspect | semantics of aspect

License

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24.241 Logic I (MIT) 24.241 Logic I (MIT)

Description

This course provides an introduction to the aims and techniques of formal logic. Logic is the science of correct argument, and our study of logic will aim to understand what makes a correct argument good, that is, what is it about the structure of a correct argument that guarantees that, if the premises are all true, the conclusion will be true as well? Our subject (though, to be sure, we can only scratch the surface) will be truth and proof, and the connection between them. This course provides an introduction to the aims and techniques of formal logic. Logic is the science of correct argument, and our study of logic will aim to understand what makes a correct argument good, that is, what is it about the structure of a correct argument that guarantees that, if the premises are all true, the conclusion will be true as well? Our subject (though, to be sure, we can only scratch the surface) will be truth and proof, and the connection between them.

Subjects

techniques of formal logic | techniques of formal logic | truth functions | truth functions | quantifiers | quantifiers | validity | validity | formal deduction | formal deduction | logic applications | logic applications | philosophy | philosophy

License

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24.979 Topics in Semantics (MIT) 24.979 Topics in Semantics (MIT)

Description

This seminar will investigate the expression of gradability, comparison and degree in natural language. The course will address the following major issues, though we may also include other topics according to the interests and direction of the class: The underlying semantic representation of expressions of degree and the linguistic significance of scalar representations The logical form of comparative constructions, and the implications of comparatives for other aspects of the grammar The semantics of degree and the role of scalar representations in grammatical categories other than gradable adjectives This seminar will investigate the expression of gradability, comparison and degree in natural language. The course will address the following major issues, though we may also include other topics according to the interests and direction of the class: The underlying semantic representation of expressions of degree and the linguistic significance of scalar representations The logical form of comparative constructions, and the implications of comparatives for other aspects of the grammar The semantics of degree and the role of scalar representations in grammatical categories other than gradable adjectives

Subjects

semantics of grading and degree | semantics of grading and degree | Vague predicates | Vague predicates | Degrees relations | Degrees relations | Scale structure | Scale structure | degree modification | degree modification | Relative gradable adjectives | Relative gradable adjectives | absolute gradable adjectives | absolute gradable adjectives | standard of comparison | standard of comparison | Scope ambiguities | Scope ambiguities | superlatives | superlatives | polar opposition | polar opposition | negative polarity | negative polarity | Comparative quantifiers | Comparative quantifiers | Partitives | Partitives | Telicity | Telicity

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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24.241 Logic I (MIT) 24.241 Logic I (MIT)

Description

Introduction to the aims and techniques of formal logic. The logic of truth functions and quantifiers. The concepts of validity and truth and their relation to formal deduction. Applications of logic and the place of logic in philosophy. Introduction to the aims and techniques of formal logic. The logic of truth functions and quantifiers. The concepts of validity and truth and their relation to formal deduction. Applications of logic and the place of logic in philosophy.

Subjects

formal logic | formal logic | truth functions | truth functions | quantifiers | quantifiers | validity | validity | truth | truth | formal deduction | formal deduction | applications of logic | applications of logic | logic in philosophy | logic in philosophy

License

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6.863J Natural Language and the Computer Representation of Knowledge (MIT) 6.863J Natural Language and the Computer Representation of Knowledge (MIT)

Description

6.863 is a laboratory-oriented course on the theory and practice of building computer systems for human language processing, with an emphasis on the linguistic, cognitive, and engineering foundations for understanding their design. 6.863 is a laboratory-oriented course on the theory and practice of building computer systems for human language processing, with an emphasis on the linguistic, cognitive, and engineering foundations for understanding their design.

Subjects

natural language processing | natural language processing | computational methods | computational methods | computer science | computer science | artificial intelligence | artificial intelligence | linguistic theory | linguistic theory | psycholinguistics | psycholinguistics | applications | applications | thematic structure | thematic structure | lexical-conceptual structure | lexical-conceptual structure | semantic structure | semantic structure | pragmatic structure | pragmatic structure | discourse structure | discourse structure | phonology | phonology | morphology | morphology | 2-level morphology | 2-level morphology | kimmo | kimmo | hmm tagging | hmm tagging | tagging | tagging | rule-based tagging | rule-based tagging | part of speech tagging | part of speech tagging | brill tagger | brill tagger | parsing | parsing | syntax | syntax | automata | automata | word modeling | word modeling | grammars | grammars | parsing algorithms | parsing algorithms | shift-reduce parsers | shift-reduce parsers | Earley's algorithm | Earley's algorithm | chart parsing | chart parsing | context-free parsing | context-free parsing | feature-based parsing | feature-based parsing | natural language system design | natural language system design | integrated lexicon | integrated lexicon | syntactic features | syntactic features | semantic interpretation | semantic interpretation | compositionality | compositionality | quantifiers | quantifiers | lexical semantic | lexical semantic | semantics | semantics | machine translation | machine translation | language learning | language learning | computational models of language | computational models of language | origins of language | origins of language | 6.863 | 6.863 | 9.611 | 9.611

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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24.241 Logic I (MIT)

Description

Introduction to the aims and techniques of formal logic. The logic of truth functions and quantifiers. The concepts of validity and truth and their relation to formal deduction. Applications of logic and the place of logic in philosophy.

Subjects

formal logic | truth functions | quantifiers | validity | truth | formal deduction | applications of logic | logic in philosophy

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.100A Introduction to Analysis (MIT)

Description

Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the pla

Subjects

mathematical analysis | estimations | limit of a sequence | limit theorems | subsequences | cluster points | infinite series | power series | local and global properties | continuity | intermediate-value theorem | convexity | integrability | Riemann integral | calculus | convergence | Gamma function | Stirling | quantifiers and negation | Leibniz | Fubini | improper integrals | Lebesgue integral | mathematical proofs | differentiation | integration

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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24.241 Logic I (MIT)

Description

This course provides an introduction to the aims and techniques of formal logic. Logic is the science of correct argument, and our study of logic will aim to understand what makes a correct argument good, that is, what is it about the structure of a correct argument that guarantees that, if the premises are all true, the conclusion will be true as well? Our subject (though, to be sure, we can only scratch the surface) will be truth and proof, and the connection between them.

Subjects

techniques of formal logic | truth functions | quantifiers | validity | formal deduction | logic applications | philosophy

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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Real Analysis I

Description

This course is designed to introduce the student to the rigorous examination of the real number system and the foundations of calculus. Analysis lies at the heart of the trinity of higher mathematics—algebra, analysis, and topology—because it is where the other two fields meet. This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Mathematics 241)

Subjects

real number | set | operations | quantifiers | bounds | irrationals | absolute values | euclidean | vectors | metric | subsequences | cauchy sequences | series | limits | differentiation | integration | integral | interchange | Computer science | I100

License

Attribution 2.0 UK: England & Wales Attribution 2.0 UK: England & Wales http://creativecommons.org/licenses/by/2.0/uk/ http://creativecommons.org/licenses/by/2.0/uk/

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6.863J Natural Language and the Computer Representation of Knowledge (MIT)

Description

6.863 is a laboratory-oriented course on the theory and practice of building computer systems for human language processing, with an emphasis on the linguistic, cognitive, and engineering foundations for understanding their design.

Subjects

natural language processing | computational methods | computer science | artificial intelligence | linguistic theory | psycholinguistics | applications | thematic structure | lexical-conceptual structure | semantic structure | pragmatic structure | discourse structure | phonology | morphology | 2-level morphology | kimmo | hmm tagging | tagging | rule-based tagging | part of speech tagging | brill tagger | parsing | syntax | automata | word modeling | grammars | parsing algorithms | shift-reduce parsers | Earley's algorithm | chart parsing | context-free parsing | feature-based parsing | natural language system design | integrated lexicon | syntactic features | semantic interpretation | compositionality | quantifiers | lexical semantic | semantics | machine translation | language learning | computational models of language | origins of language | 6.863 | 9.611

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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24.979 Topics in Semantics (MIT)

Description

This seminar will investigate the expression of gradability, comparison and degree in natural language. The course will address the following major issues, though we may also include other topics according to the interests and direction of the class: The underlying semantic representation of expressions of degree and the linguistic significance of scalar representations The logical form of comparative constructions, and the implications of comparatives for other aspects of the grammar The semantics of degree and the role of scalar representations in grammatical categories other than gradable adjectives

Subjects

semantics of grading and degree | Vague predicates | Degrees relations | Scale structure | degree modification | Relative gradable adjectives | absolute gradable adjectives | standard of comparison | Scope ambiguities | superlatives | polar opposition | negative polarity | Comparative quantifiers | Partitives | Telicity

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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24.921 Special Topics in Linguistics: Genericity (MIT)

Description

This course will investigate the semantics of generic sentences, i.e., sentences that are used to talk about habits, tendencies, dispositions, or kinds. For instance: Dogs are good pets. The giant panda is an endangered species. A soccer player makes lots of money. Mary smokes after dinner. This machine crushes oranges. This is a half-semester course.

Subjects

semantics of generic sentences | modality | adverbial quantifiers | semantics of aspect

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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Discrete Structures

Description

This course describes discrete mathematics, which involves processes that consist of sequences of individual steps (as compared to calculus, which describes processes that change in a continuous manner). The principal topics presented in this course are logic and proof, induction and recursion, discrete probability, and finite state machines. This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Computer Science 202)

Subjects

discrete structures | truth tables | negations | tautologies | conditional statements | modus ponens | modus tollens | generalization | specialization | elimination | quantified | quantifiers | number theory | divisibility | induction | sequences | notation | set theory | recursion | automata | Computer science | I100

License

Attribution 2.0 UK: England & Wales Attribution 2.0 UK: England & Wales http://creativecommons.org/licenses/by/2.0/uk/ http://creativecommons.org/licenses/by/2.0/uk/

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