Abstract In logic, a theory is a deductively closed set of sentences. Theories containing all logical theorems are called regular, while irregular theories omit at least one logical theorem. We argue that the widespread assumption that theories must be regular is misguided. This is because (1) philosophical sense can be made of irregular theories when thinking of theories as modeling trasmission of commitment and (2) standard reasons for only considering regular theories are either question-begging or unnecessarily limit what theories can be used for.
Mangraviti et al. (2026) studied this question.