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Ai Taniguchi is a linguist specializing in formal semantics and pragmatics. Her University of Toronto Mississauga profile describes research on kinds of meaning beyond an utterance's literal main assertion, including social meaning and how context changes interpretation.^[ref]

This distinguishes what a sentence directly asserts from information conveyed through its use and context. Formal models make those proposed differences explicit enough to compare against linguistic examples. She is a coauthor of Essentials of Linguistics (2nd edition) by Catherine Anderson and others and uses comics and visual art for public communication about linguistics, as documented in the same institutional profile.

Formal semantics describes linguistic meaning with explicit mathematical representations and rules for combining them. A truth condition states when a declarative expression is true in a model; compositional semantics explains how meanings depend on both the parts and their arrangement. A syntactic category alone need not determine the semantic operation.^[ref]

In a toy model, let $B=\{1,2\}$ denote the boxes and $R=\{2,3\}$ the red objects. “Every box is red” is true exactly when $B\subseteq R$, which fails here. “Some box is red” is true when $B\cap R\ne \varnothing$, which holds. The difference comes from the quantifier's rule, not a change in the noun's denotation. Such finite examples make competing semantic proposals testable while leaving conversational interpretation to additional assumptions about context and pragmatics.

A truth condition specifies what must hold for a declarative expression to be true under an interpretation and context. It is distinct from the expression's actual truth value: someone can understand what would make a statement true without knowing whether those circumstances obtain.^[ref]

For a toy example, interpret Every marked tile is blue using a set $M$ of marked tiles and a set $B$ of blue tiles. Its truth condition is $M\subseteq B$. If $M=\{1,2\}$ and $B=\{2,3\}$, it is false; changing $B$ to $\{1,2,3\}$ makes it true. The rule remains fixed while the model changes. Truth conditions allow formal semantics to separate an interpretation from the evidence used to assess a particular situation, although pragmatics can contribute further conversational meaning.