How did Charles Sanders Peirce connect logic with semiotics?

Charles Sanders Peirce connected logic with semiotics by identifying the former, in its widest sense, as the general theory of signs. He viewed the study of sign action, or semiosis, as fundamental to logical inquiry, intending to title his major unfinished work A System of Logic, Considered as Semiotic.1

Peirce’s approach integrated these fields by grounding his semiotic theories in pragmatism and the logic of science. He utilized his system of categories—Firstness, Secondness, and Thirdness—to provide a systematic framework for both his logical divisions (such as abduction, induction, and deduction) and his classification of signs into icons, indexes, and symbols. By treating logic as a branch of semiotics, Peirce sought to establish a comprehensive method for understanding how signs function in the formation of beliefs and the pursuit of scientific knowledge.12