Given a raw knowledge in the form of a data table/a decision system, one is facing two possible venues. One, to treat the system as closed, i.e., its universe does not admit new objects, or, to the contrary, its universe is open on admittance of new objects. In particular, one may obtain new objects whose sets of values of features are new to the system. In this case the problem is to assign a decision value to any such new object. This problem is somehow resolved in the rough set theory, e.g., on the basis of similarity of the value set of a new object to value sets of objects already assigned a decision value. It is crucial for online learning when each new object must have a predicted decision value.\ There is a vast literature on various methods for decision prediction for new yet unseen object. The approach we propose is founded in the theory of rough mereology and it requires a theory of sets/concepts, and, we root our theory in classical set theory of Syllogistic within which we recall the theory of parts known as Mereology. Then, we recall our theory of Rough Mereology along with the theory of weight assignment to the Tarski algebra of Mereology.\ This allows us to introduce the notion of a part to a degree. Once we have defined basics of Mereology and rough Mereology, we recall our theory of weight assignment to elements of the Boolean algebra within Mereology and this allows us to define the relation of parts to the degree and we apply this notion in a procedure to select a decision for new yet unseen objects.\ In selecting a plausible candidate which would pass its decision value to the new object, we employ the notion of Vapnik - Chervonenkis dimension in order to select at the first stage the candidate with the largest VC-dimension of the family of its $\varepsilon$-components for some choice of $\varepsilon$.

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).