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Questions and Answers
What does a truth table for negation indicate about the truth value of a proposition?
What does a truth table for negation indicate about the truth value of a proposition?
Which truth table accurately reflects the operation of conjunction?
Which truth table accurately reflects the operation of conjunction?
In the context of inclusive disjunction, which scenario results in a false outcome?
In the context of inclusive disjunction, which scenario results in a false outcome?
What is the result of the material implication p → q when p is false?
What is the result of the material implication p → q when p is false?
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Which description best fits the biconditional connective p ≡ q?
Which description best fits the biconditional connective p ≡ q?
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What does the correspondence theory of truth primarily focus on?
What does the correspondence theory of truth primarily focus on?
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What is the primary objective of model-theoretic semantics?
What is the primary objective of model-theoretic semantics?
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In the denotational approach, what is the primary function of language?
In the denotational approach, what is the primary function of language?
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What term describes the relationship when the truth of one proposition guarantees the truth of another?
What term describes the relationship when the truth of one proposition guarantees the truth of another?
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In the context of propositions, what does mutual entailment imply?
In the context of propositions, what does mutual entailment imply?
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What occurs when two propositions cannot be true at the same time?
What occurs when two propositions cannot be true at the same time?
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Which example illustrates lexical ambiguity in a sentence?
Which example illustrates lexical ambiguity in a sentence?
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What is the focus of the Principle of Compositionality in semantics?
What is the focus of the Principle of Compositionality in semantics?
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Which of the following statements correctly embodies the principle of recursion in grammar?
Which of the following statements correctly embodies the principle of recursion in grammar?
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What defines a verb phrase structure in grammar?
What defines a verb phrase structure in grammar?
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Which of the following best describes syntactic ambiguity?
Which of the following best describes syntactic ambiguity?
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What does the subscript ‘n’ in the model notation Mn represent?
What does the subscript ‘n’ in the model notation Mn represent?
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In the model M1, which statement is true about the sentence 'Harry danced'?
In the model M1, which statement is true about the sentence 'Harry danced'?
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Which of the following best defines an implication in the context of inferential relationships?
Which of the following best defines an implication in the context of inferential relationships?
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What role does the lexical item 'anymore' play in the implication example provided?
What role does the lexical item 'anymore' play in the implication example provided?
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Which expression represents the evaluation of the sentence 'S(h)' in model M1?
Which expression represents the evaluation of the sentence 'S(h)' in model M1?
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With regard to verb phrase structures, which characteristic is essential for understanding sentences within a model?
With regard to verb phrase structures, which characteristic is essential for understanding sentences within a model?
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In terms of recursion in grammar, which statement accurately reflects its importance?
In terms of recursion in grammar, which statement accurately reflects its importance?
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Which aspect is not typically associated with ambiguity in syntax?
Which aspect is not typically associated with ambiguity in syntax?
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Study Notes
HSL747: Language Computations and Mental Architecture
- Course offered by Deepak Alok at IIT Delhi, Semester 1, 2024-2025
Syntax
- Syntax is the study of how words are arranged in sentences, clauses, and phrases to create grammatically sound expressions in a language.
- Examples show substitution of nouns (e.g., man with woman, dog, king), but not other word types (e.g., green, in, sing).
Parts of Speech
- Traditionally, parts of speech are defined semantically
- Nouns are "person, place, or thing"
- Verbs are "action, state, or state of being"
- Traditional definitions aren't suitable for all words (e.g., Destruction, Assassination).
- Some words can change syntactic category based on surrounding words (e.g., pen).
Problems with Traditional Definitions
- Traditional definitions don't work well for words like “destruction” and “assassination,” which function as nouns yet describe actions. Words like “think” and “believe” are verbs that don't seem to describe actions.
Parts of speech/lexical category
- Parts of speech tell us how a word functions within a sentence.
Distributional Criteria
- Two methods exist for determining a word's part of speech using Distributional Criteria:
- Morphological - examining affixes (e.g., suffixes like -ment, -ness or -ation, ...)
- Syntactic - analyzing where a word appears in a sentence and the surrounding words (e.g., a big house).
Open vs. Closed Categories
- Open categories include Nouns, Verbs, Adjectives and Adverbs (can be extended).
- Closed categories are hard or impossible to extend, and encode grammatical information like articles (e.g., a, an, the) or prepositions (e.g., in).
Constituents
- A constituent is a group of words that functions as a unit in syntax.
- Phrases (e.g., noun phrases, verb phrases, prepositional phrases, adjective phrases) are types of constituents.
- Sentence structure is built from constituents (not individual words).
Prepositional Phrases (PPs)
- PPs are units that typically contain a preposition and a noun phrase (e.g., on the table, in the woods).
- One or more PPs can occur in a noun phrase (e.g., the dog from the window).
Adjective and Adverb Phrases (AdjP, AdvP)
- Adjectives (e.g., big, yellow) typically modify a noun (and occur in an AdjP) that is often found in between a determiner and a noun.
- Adverbs (e.g., quickly, happily) often modify verbs, adjectives, other adverbs (frequently, very), and commonly occur in an AdvP.
Recursion
- Recursion is the ability of a structure to include a copy of itself within the structure (e.g., a phrase occurring within a phrase, recursively).
Ambiguity
- A sentence or phrase can have more than one constituent structure (syntactic tree). This leads to multiple interpretations of the meaning and therefore is considered ambiguous.
Verb Phrases (VPs)
- A VP comprises a verb and its arguments (e.g., [V NP], [V NP NP], [V CP]).
- Nouns are often arguments in sentences, and they can occur more than once in a VP, depending on the verb.
- For example: [VP eat], [VP read the book], [VP give the boy a book]
CP (Complementizer Phrases)
- A CP can be optional in a sentence. Some VP's have clauses (CPs) instead of a noun as arguments (e.g., I told you that you are correct).
- Sometimes verbs follow a clause that begins with words like if, that, or whether (ex: I will see if you are available.
Sentences (S/TP)
- Sentences (S) or Tense Phrases (TP) generally contain a noun phrase and verb phrase.
- For example: Mary can sing (Mary: NP ; can sing: VP).
PP (Prepositional Phrases)
- PPs are part of phrases, like the table on top, across the river; or can be a stand alone constituent like up, down, etc.
- The structure for PPs is P–(NP)
Conjunctions
- Conjunctions are useful in connecting words, phrases and sometimes, sentences.
- These structures can include connectives like and, or but, if, unless, etc. ; thus creating more complex sentences.
Phrase Structure Rules (PSRs)
- A set of rules to describe possible grammatical sentences for a language.
Constituency Tests
- Three tests that are useful for identifying constituents in a sentence:
- Fragment Test: A constituent can stand alone as an answer to a question.
- Substitution Test: A constituent can be replaced by an equivalent word or phrase.
- Movement Test: A constituent can be moved around in a sentence.
Analyzing a Sentence with Syntax Trees
- Construct a tree of a sentence using phrases and lexical categories, keeping in mind possible constituents and structure.
Other Languages
- The order of constituents may differ across languages.
Semantic Features
- Words have semantic features to describe their properties (e.g., woman includes human and female).
- Verbs have semantic features to describe action (e.g., transitive verbs take one or more noun phrases after the verb).
- Features like active vs. stative, change of state, or iteratives give verb descriptions further specificity.
- Nouns can be morphologically marked, and semantic features of different words can indicate how they relate to each other in meaning.
Compositional Semantics
- Proposition(s) - This is a claim that can be either true or false in the world.
- Truth Value - Whether a proposition is true or false in a given world.
- Entailment - A relationship between two propositions or sentences where the truth of one (A) logically guarantees the truth of another (B).
- Incompatibility - A relationship between two propositions or sentences where the truth of one logically excludes the truth of another.
Semantic Rules
- Defining a consistent set of rules that can be used to determine the meaning of a complex set of words within a sentence.
Idomatic Meaning
- A phrase that has a specific meaning that cannot be deduced from the meaning of the constituent words.
Proper Nouns
- Words that refer to unique individuals in the world.
Common Nouns
- Words that refer to a category of individuals in the world.
Inferences
- entailment
- presupposition
- implicature
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