lecture 1 introduction to formal semantics and compositionality

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Okay, let's dive into a comprehensive tutorial on Lecture 1: Introduction to Formal Semantics and Compositionality. I'll cover the core concepts, motivations, and provide practical examples, including code snippets where relevant (primarily using Python and potentially some logic libraries).

*Lecture 1: Introduction to Formal Semantics and Compositionality*

*1. What is Semantics?*

At its most fundamental, semantics is the study of meaning. In linguistics and computer science, we're interested in understanding:

*Meaning of words (lexical semantics):* What does "cat" mean? What are its properties? How does it relate to other words like "animal" or "feline"?
*Meaning of sentences (sentential semantics):* What does "The cat sat on the mat" mean? Not just the individual words, but how they combine to express a complete thought.
*Meaning of larger texts/discourses:* How do sentences connect and contribute to an overall message in a conversation, a paragraph, or an entire book?
*How meaning relates to truth (truth-conditional semantics):* Under what circumstances is a sentence true or false?
*How meaning relates to context (pragmatics):* How does the meaning of an utterance change depending on who's speaking, the situation, and the shared knowledge of the participants?

*2. Why Formal Semantics?*

Natural Language is notoriously ambiguous and messy. To get computers to understand and reason about language, we need a more precise, formal way to represent meaning. Formal semantics aims to:

*Provide a rigorous and unambiguous description of meaning:* Move beyond vague intuitions and offer a structured system for representing the meaning of sentences.
*Allow for computational manipulation of meaning:* Enable computers to reason about language, answer questions, translate between languages, and more.
*Make predictions about meaning:* Formal theories can predict how the meaning of a sentence will change if we modif ...

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