Epistemic Syllogistic: First Steps

Although modal logic is regarded as a relatively young field, its origins can be traced back to Aristotle, who explored syllogistic reasoning patterns that incorporated modalities. However, in contrast to his utterly successful assertoric syllogistic, Aristotle's examination of modal syllogisms is often viewed as error-prone and controversial, thus receiving less attention from logicians. In the literature, a large body of research on Aristotle's modal syllogistic primarily centers on the possibility of a coherent interpretation of his proposed modal systems grounded by his philosophy on necessity and contingency (see, e.g., [11, 5, 12]). We adopt a more liberal view on Aristotle's modal syllogistic, considering it as a source of inspiration for formalizing natural reasoning patterns involving modalities, rather than scrutinizing the coherence of the original systems. Our approach is encouraged by the fruitful research program of natural logic, which explores "light" logic systems that admit intuitive reasoning patterns in natural languages while balancing expressivity and computational complexity [1, 8]. In particular, various extensions of the assertoric syllogistic have been proposed and studied [8]. In this paper, we propose a systematic study on epistemic syllogistic to initiate our technical investigations of (extensions of) modal syllogistic. The choice for the epistemic modality is intentional for its ubiquitous use in natural languages. Consider the following syllogism: All C are B Some C is known to be A Some B is known to be A Taking the intuitive de re reading, the second premise and the conclusion above can be formalized as x(Cx KAx) and x(Bx KAx) respectively in first-order modal logic (FOML).