Compositional semantics is all about how we build meaning from smaller parts. It's like putting together a puzzle, where each word is a piece and the rules of grammar are the instructions.

This topic dives into how we combine words to create phrases and sentences. It explores the challenges we face when dealing with tricky language like idioms and metaphors, and how context plays a big role in understanding.

Compositional Semantics

Principles and Foundations

• Compositional semantics determines complex expression meanings from constituent parts and combination rules
• Principle of Compositionality (Gottlob Frege) defines complex expression meaning as a function of part meanings and combination mode
• Semantic composition combines word or phrase meanings to derive larger linguistic unit meanings (sentences)
• Assumes language systematicity with regular meaning combination patterns
• Utilizes recursive processes allowing infinite novel sentences from finite words and rules
• Formal semantic theories (model-theoretic semantics) provide mathematical frameworks for compositional meaning representation and computation
• Faces challenges with idioms, metaphors, and context-dependent expressions requiring additional semantic mechanisms

Semantic Composition Process

• Combines individual word meanings to form phrase meanings
• Builds up sentence meaning from constituent phrase meanings
• Applies composition rules based on syntactic structure
• Accounts for word order and grammatical relationships
• Resolves ambiguities through contextual information
• Integrates world knowledge and pragmatic factors
• Handles non-literal language (metaphors, idioms) through specialized mechanisms

Compositionality Challenges

• Idioms resist strict compositional analysis ("kick the bucket" ≠ physically kicking a bucket)
• Metaphors require mapping between conceptual domains ("time is money")
• Context-dependent expressions change meaning based on situation ("it's cold" relative to speaker/location)
• Coercion phenomena force meaning shifts ("enjoy the book" implies reading, not physical object)
• Quantifier scope ambiguities lead to multiple interpretations ("every student read a book")
• Presuppositions and implicatures contribute meaning beyond literal composition
• Vague or underspecified meanings require contextual resolution ("tall" relative to comparison class)

Syntax and Meaning

Syntactic Structure and Semantic Interpretation

• Syntax provides structural framework for semantic composition
• Determines word and phrase combination into larger meaningful units
• Semantic compositionality ties closely to syntactic structure
• Complex expression meaning depends on syntactic configuration
• Syntactic categories (nouns, verbs, adjectives) constrain possible semantic interpretations
• Phrase structure rules and syntactic trees represent hierarchical organization of expressions
• Guides semantic composition process through structural relationships

Syntactic Ambiguity and Meaning

• Syntactic ambiguity leads to multiple semantic interpretations of single sentences
• Structural ambiguity arises from different possible phrase attachments ("I saw the man with the telescope")
• Lexical category ambiguity occurs when words have multiple syntactic roles ("bank" as noun or verb)
• Coordination ambiguity results from unclear scope of conjunctions ("old men and women")
• Garden path sentences temporarily mislead readers due to initial incorrect parsing ("The horse raced past the barn fell")
• Resolution often requires context, world knowledge, or pragmatic reasoning

Argument Structure and Semantic Roles

• Argument structure specifies number and types of semantic arguments for predicates
• Influences overall sentence meaning through participant relationships
• Thematic roles (Agent, Patient, Theme) assign semantic functions to syntactic positions
• Transitivity alternations affect argument realization and interpretation ("The vase broke" vs. "John broke the vase")
• Syntactic operations (passivization, causativization) modify argument structure and semantic focus
• Verb classes (unaccusative, unergative) determine allowable argument patterns
• Theta criterion ensures one-to-one mapping between semantic roles and syntactic positions

Function vs Content Words

Content Words: Lexical Meaning Contributors

• Carry substantive semantic content in expressions
• Include nouns, verbs, adjectives, and adverbs
• Nouns denote entities, objects, or abstract concepts ("cat," "freedom")
• Verbs express actions, states, or processes ("run," "think")
• Adjectives describe properties or attributes ("red," "intelligent")
• Adverbs modify verbs, adjectives, or other adverbs ("quickly," "very")
• Open class allows new members to be added to the lexicon
• Contribute to propositional content and truth conditions of sentences

Function Words: Grammatical and Structural Elements

• Serve primarily grammatical purposes in sentences
• Contribute to structural meaning and relationships
• Include determiners, prepositions, conjunctions, and auxiliaries
• Determiners specify reference and quantification of noun phrases ("the," "some")
• Prepositions encode spatial, temporal, or other relations ("in," "on," "by")
• Conjunctions combine phrases or clauses ("and," "but," "because")
• Auxiliaries provide tense, aspect, and modality information ("have," "will," "must")
• Closed class with limited membership and infrequent additions
• Essential for creating grammatical and coherent expressions

Interaction and Semantic Contribution

• Function words modify or specify semantic contribution of content words
• Quantifiers (function words) determine scope and interpretation of noun phrases ("every," "some")
• Determiners affect referential properties and discourse status of entities ("the" vs. "a")
• Prepositions link content words to create complex semantic structures ("the book on the table")
• Conjunctions establish logical relationships between propositions ("It's raining, so the ground is wet")
• Tense and aspect markers (function words) situate events in time and specify their internal structure
• Modals contribute to the expression of possibility, necessity, and obligation ("can," "should")
• Negation words alter truth values and create scope ambiguities ("not," "never")

Interpreting Sentence Meaning

Lexical and Syntactic Analysis

• Identify lexical meanings of individual words, distinguishing denotations from connotations
• "Bank" denotation financial institution, connotation stability or wealth
• Analyze syntactic structure, determining hierarchical relationships between words and phrases
• Create syntactic tree representing constituent structure (S → NP VP)
• Recognize syntactic categories and their combinatorial properties (Adjective + Noun, Verb + Object)
• Resolve structural ambiguities based on context or preferred interpretations
• "The man saw the girl with the telescope" attachment ambiguity

Semantic Composition and Ambiguity Resolution

• Apply semantic composition rules to combine constituent meanings
• Start from lowest levels of syntactic tree, working upwards
• Adjective + Noun: intersective ("red ball") vs. subsective ("skillful surgeon")
• Verb + Arguments: fill thematic roles based on verb semantics ("John gave Mary the book")
• Resolve semantic ambiguities considering possible interpretations
• Lexical ambiguity: "bank" financial institution or river edge
• Scope ambiguity: "Every student read a book" (one book or multiple)
• Select most appropriate interpretation based on context or world knowledge
• "The pen is in the box" likely writing instrument, not animal enclosure

Non-compositional Elements and Truth Conditions

• Identify and interpret non-compositional elements (idioms, metaphors)
• Idioms: "kick the bucket" interpreted as "die" rather than literal meaning
• Metaphors: "Time is money" understood through conceptual mapping
• Integrate non-compositional meanings into overall sentence interpretation
• Account for pragmatic implicatures and presuppositions
• "Some students passed" implicates not all students passed
• "The king of France is bald" presupposes existence of French king
• Evaluate truth conditions based on composed meaning
• Consider how sentence relates to possible states of affairs in world
• "The cat is on the mat" true if and only if there exists a cat located on a mat