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).

In this paper, we propose a lightweight yet powerful dynamic epistemic logic that captures not only the distinction between de dicto and de re knowledge but also the distinction between de dicto and de re updates. The logic is based on the dynamified version of an epistemic language extended with the assignment operator borrowed from dynamic logic, following the work of Wang and Seligman (Proc. AiML 2018). We obtain complete axiomatizations for the counterparts of public announcement logic and event-model-based DEL based on new reduction axioms taking care of the interactions between dynamics and assignments.

Various planning-based know-how logics have been studied in the recent literature. In this paper, we use such a logic to do know-how-based planning via model checking. In particular, we can handle the higher-order epistemic planning involving know-how formulas as the goal, e.g., find a plan to make sure p such that the adversary does not know how to make p false in the future. We give a PTIME algorithm for the model checking problem over finite epistemic transition systems and axiomatize the logic under the assumption of perfect recall.

In this paper, we study the model theoretical aspects of Weakly Aggregative Modal Logic (WAL), which is a collection of disguised polyadic modal logics with $n$-ary modalities whose arguments are all the same. We give a van-Benthem-Rosen characterization theorem of WAL based on an intuitive notion of bisimulation, and show that WAL has Craig Interpolation.

In standard epistemic logic, agent names are usually assumed to be common knowledge. This is unreasonable for various applications. Inspired by term modal logic and assignment operators in dynamic logic, we introduce a lightweight modal predicate logic whose names are not rigid. The language can handle various de dicto/de re distinctions in a natural way. We show the decidability of the logic over arbitrary models and give a complete axiomatization over S5 models.

A true lie is a lie that becomes true when announced. In a logic of announcements, where the announcing agent is not modelled, a true lie is a formula (that is false and) that becomes true when announced. We investigate true lies and other types of interaction between announced formulas, their preconditions and their postconditions, in the setting of Gerbrandy's logic of believed announcements, wherein agents may have or obtain incorrect beliefs. Our results are on the satisfiability and validity of instantiations of these semantically defined categories, on iterated announcements, including arbitrarily often iterated announcements, and on syntactic characterization. We close with results for iterated announcements in the logic of knowledge (instead of belief), and for lying as private announcements (instead of public announcements) to different agents. Detailed examples illustrate our lying concepts.

When we say "I know why he was late", we know not only the fact that he was late, but also an explanation of this fact. We propose a logical framework of "knowing why" inspired by the existing formal studies on why-questions, scientific explanation, and justification logic. We introduce the Ky_i operator into the language of epistemic logic to express "agent i knows why phi" and propose a Kripke-style semantics of such expressions in terms of knowing an explanation of phi. We obtain two sound and complete axiomatizations w.r.t. two different model classes depending on different assumptions about introspection.

In this paper, we propose a single-agent modal logic framework for reasoning about goal-direct "knowing how" based on ideas from linguistics, philosophy, modal logic and automated planning. We first define a modal language to express "I know how to guarantee phi given psi" with a semantics not based on standard epistemic models but labelled transition systems that represent the agent's knowledge of his own abilities. A sound and complete proof system is given to capture the valid reasoning patterns about "knowing how" where the most important axiom suggests its compositional nature.

Knowing whether a proposition is true means knowing that it is true or knowing that it is false. In this paper, we study logics with a modal operator Kw for knowing whether but without a modal operator K for knowing that. This logic is not a normal modal logic, because we do not have Kw (phi -> psi) -> (Kw phi -> Kw psi). Knowing whether logic cannot define many common frame properties, and its expressive power less than that of basic modal logic over classes of models without reflexivity. These features make axiomatizing knowing whether logics non-trivial. We axiomatize knowing whether logic over various frame classes. We also present an extension of knowing whether logic with public announcement operators and we give corresponding reduction axioms for that. We compare our work in detail to two recent similar proposals.