The paper introduces a dynamic semantic interpretation of first-order predicate logic, referred to as "dynamic predicate logic" (DPL). This approach aims to develop a compositional, non-representational theory of discourse semantics, addressing the issue of non-compositionality in existing theories. The authors argue that compositionality is a methodological principle rather than an empirical one and focus on developing a compositional alternative that is empirically equivalent to non-compositional theories. The dynamic interpretation of DPL is inspired by dynamic logic used in programming language semantics, where the meaning of a sentence is seen as the way it changes the information of the interpreter. This dynamic view contrasts with the standard interpretation of predicate logic, which treats the meaning of a sentence as its truth conditions. The paper discusses the interpretation of various logical connectives and quantifiers in DPL, including existential quantification, conjunction, implication, universal quantification, negation, and disjunction. It provides formal definitions and examples to illustrate how these components handle cross-sentential anaphora and donkey sentences, which are challenging in standard predicate logic due to their scope and binding properties. Key features of DPL include: - **Internal and External Dynamics**: Connectives like conjunction and existential quantification can pass on variable bindings from one conjunct to another, both internally and externally. - **Universal Quantification**: Functions as a test, passing on assignments that meet certain conditions. - **Implication**: Allows existential quantifiers in the antecedent to bind variables in the consequent, with universal force. - **Negation and Disjunction**: Static in nature, blocking anaphoric links between terms and variables. The paper concludes by formally defining the syntax and semantics of DPL, introducing notions of truth, validity, contradiction, satisfaction sets, production sets, and equivalence. It highlights the differences between standard logical equivalence and the more nuanced notions of s-equivalence and p-equivalence in DPL.The paper introduces a dynamic semantic interpretation of first-order predicate logic, referred to as "dynamic predicate logic" (DPL). This approach aims to develop a compositional, non-representational theory of discourse semantics, addressing the issue of non-compositionality in existing theories. The authors argue that compositionality is a methodological principle rather than an empirical one and focus on developing a compositional alternative that is empirically equivalent to non-compositional theories. The dynamic interpretation of DPL is inspired by dynamic logic used in programming language semantics, where the meaning of a sentence is seen as the way it changes the information of the interpreter. This dynamic view contrasts with the standard interpretation of predicate logic, which treats the meaning of a sentence as its truth conditions. The paper discusses the interpretation of various logical connectives and quantifiers in DPL, including existential quantification, conjunction, implication, universal quantification, negation, and disjunction. It provides formal definitions and examples to illustrate how these components handle cross-sentential anaphora and donkey sentences, which are challenging in standard predicate logic due to their scope and binding properties. Key features of DPL include: - **Internal and External Dynamics**: Connectives like conjunction and existential quantification can pass on variable bindings from one conjunct to another, both internally and externally. - **Universal Quantification**: Functions as a test, passing on assignments that meet certain conditions. - **Implication**: Allows existential quantifiers in the antecedent to bind variables in the consequent, with universal force. - **Negation and Disjunction**: Static in nature, blocking anaphoric links between terms and variables. The paper concludes by formally defining the syntax and semantics of DPL, introducing notions of truth, validity, contradiction, satisfaction sets, production sets, and equivalence. It highlights the differences between standard logical equivalence and the more nuanced notions of s-equivalence and p-equivalence in DPL.