Dynamic predicate logic (DPL) is a compositional semantic framework for first-order predicate logic, designed to address challenges in discourse semantics, particularly cross-sentential anaphora and donkey sentences. Unlike traditional model-theoretic semantics, which often rely on static truth conditions, DPL treats meaning as dynamic, focusing on how information is transformed during interpretation. This approach allows for a more natural and compositional treatment of anaphoric relations, where pronouns and indefinite terms are bound by quantifiers across sentence boundaries. The paper introduces DPL as an alternative to discourse representation theory (DRT), which, while successful in handling these phenomena, lacks compositional structure. DPL provides a dynamic interpretation of logical connectives and quantifiers, enabling the compositional treatment of anaphora and binding. For example, existential quantification in DPL allows variables to be bound across multiple conjuncts, facilitating the interpretation of sentences like "Every farmer who owns a donkey beats it." Key components of DPL include dynamic conjunction, which passes variable bindings from one part of a sentence to another, and dynamic implication, which allows existential quantifiers in the antecedent to bind variables in the consequent. Universal quantification in DPL is also dynamically interpreted, ensuring that variables bound within a quantifier remain available for subsequent parts of a sentence. The dynamic semantics of DPL is formalized through a set of rules that define the interpretation of logical expressions as sets of assignment pairs. These pairs represent possible input-output transformations during interpretation. This framework allows for a compositional and computationally plausible treatment of discourse semantics, enabling the translation of natural language sentences into logical forms that respect the dynamic nature of meaning. The paper also discusses the logical properties of DPL, including truth, validity, and equivalence. It shows that DPL can handle complex anaphoric and quantificational phenomena in a way that is both compositional and empirically equivalent to non-compositional approaches. By treating meaning as a dynamic process, DPL offers a more flexible and principled alternative to traditional semantic theories, with potential applications in both theoretical linguistics and computational semantics.Dynamic predicate logic (DPL) is a compositional semantic framework for first-order predicate logic, designed to address challenges in discourse semantics, particularly cross-sentential anaphora and donkey sentences. Unlike traditional model-theoretic semantics, which often rely on static truth conditions, DPL treats meaning as dynamic, focusing on how information is transformed during interpretation. This approach allows for a more natural and compositional treatment of anaphoric relations, where pronouns and indefinite terms are bound by quantifiers across sentence boundaries. The paper introduces DPL as an alternative to discourse representation theory (DRT), which, while successful in handling these phenomena, lacks compositional structure. DPL provides a dynamic interpretation of logical connectives and quantifiers, enabling the compositional treatment of anaphora and binding. For example, existential quantification in DPL allows variables to be bound across multiple conjuncts, facilitating the interpretation of sentences like "Every farmer who owns a donkey beats it." Key components of DPL include dynamic conjunction, which passes variable bindings from one part of a sentence to another, and dynamic implication, which allows existential quantifiers in the antecedent to bind variables in the consequent. Universal quantification in DPL is also dynamically interpreted, ensuring that variables bound within a quantifier remain available for subsequent parts of a sentence. The dynamic semantics of DPL is formalized through a set of rules that define the interpretation of logical expressions as sets of assignment pairs. These pairs represent possible input-output transformations during interpretation. This framework allows for a compositional and computationally plausible treatment of discourse semantics, enabling the translation of natural language sentences into logical forms that respect the dynamic nature of meaning. The paper also discusses the logical properties of DPL, including truth, validity, and equivalence. It shows that DPL can handle complex anaphoric and quantificational phenomena in a way that is both compositional and empirically equivalent to non-compositional approaches. By treating meaning as a dynamic process, DPL offers a more flexible and principled alternative to traditional semantic theories, with potential applications in both theoretical linguistics and computational semantics.