Dialectical logic, which takes dialectical thinking as its object of study, occupies a controversial position between logic and philosophy. The reductionist approach employed by modern logical positivists often fails to align with speculative philosophy’s interpretation of dialectical thinking, while speculative philosophy, influenced by holism, tends to rely on qualitative interpretations that lack the precise quantitative analysis required for acceptance in modern logic. Against this backdrop, and in accordance with the interdisciplinary perspective advocated by complexity science, dialectical thinking should be regarded as a subject of interdisciplinary research bridging modern logic and speculative philosophy. This new model of dialectical logic involves using the reductionist methods of modern logic to dissect the components of the complex systems referred to by dialectical concepts, identifying the relationships among these components, and then returning to a holistic speculative philosophical perspective to define the dialectical nature of the system as a whole through formalized means.

There are two main contrasting theories of names that address the relationship between names and referents: the descriptive theory and the direct reference theory. The former posits that names refer to objects through associated senses or characteristic descriptions, while the latter maintains that names function as labels and directly refer to objects without relying on senses or characteristic descriptions. Both theories initially focus on proper names and subsequently extend their principles to common names. The primary difference between the two lies in referring modes. However, debates between their proponents often revolve around whether proper and common names carry senses, which diverges from the core issue. From the perspective of referring modes, names can be classified as either direct or indirect. Every language has its own unique lexical system that includes primitive names and defined names, which correspond respectively to direct names and indirect names. The direct reference theory is a theory of names associated with direct names, while the descriptive theory is one related to indirect names. The debate over whether proper or common names contain senses is misleading. While this issue has historical roots, the modern theory of names should strive to move beyond these historical limitations.

Pragmatic logic is an interdisciplinary domain between logic and linguistics. Its evolutionary trajectory can be encapsulated through “two approaches,” “three schemes,” and “four stages.” The “two approaches” comprise pragmaticalization, featuring a transition from normative to descriptive research, and depragmaticalization, featuring a transition from descriptive to normative research. The “three schemes” consist of zero-pragmatic deductive logic, quasi-pragmatic inductive logic, and pragmatic informal logic. The “four stages” include “genesis of pragmatics,” “depragmaticalization,” “quasi-pragmaticalization,” and “return to pragmatics.” So far, the two research approaches of pragmatic logic appear to evolve independently with mutual incommensurability and primarily focus on addressing pragmatic issues. To significantly advance the field of pragmatic logic, it is essential to unify the two traditional approaches to explore a new developmental direction.

Metaphor is pervasive in everyday life, and it not only serves as a linguistic rhetoric but also functions as a vital cognitive mechanism. Relevance theory (RT), grounded in the ad hoc concept and the principle of relevance, provides an illuminating approach to analyzing linguistic metaphors. However, challenges persist in achieving its formal analysis. Game-theoretic pragmatics (GTP) introduces mathematical models and solution approaches to analyze interactive decision-making among multiple participants in language use. The Iterated Best Response (IBR) model, within this domain, effectively illustrates from an internal perspective how communicators achieve equilibrium (the correct understanding of an expression), thus providing advantageous conditions for systematic and comprehensive formal analyses of RT. This article employs the IBR model as a fundamental tool to investigate the interaction processes among various elements in metaphor usage. It constructs a holistic formal analysis framework, offering innovative approaches for the formal interpretation of metaphors.

Informal logic emerged as a new branch when modern logic reached its heyday, focusing on practical argumentation to overcome the limitations inherent in rigorous formal deductive logic for analyzing and evaluating natural language arguments. Its fundamental purpose is to redirect logical inquiry towards practical concerns, distinguishing sound and fallacious arguments. Since the 1960s, informal logic has evolved into a mature theory in the West and has been widely applied across various fields. Informal logic was introduced to China in the late 1980s, and the understanding of its theoretical system and nature in Chinese academia has undergone a spiraling upward development process. Motivated by the practical needs for analyzing and evaluating real arguments through informal reasoning, the Chinese scholars, on the foundation of extensive introduction and investigation of informal logic, have also proposed some new understandings and perspectives on its core issues by integrating contemporary cultural context. It has significantly contributed to the pluralistic development of informal logic in the contemporary era.

According to a version of logical hylomorphism that is derived from Kant and has become popular along with the use of modern logic techniques, the validity of reasoning is a purely formal validity completely independent of content, and logic’s concern with such formality is the primary characteristic that distinguishes it from other disciplines. However, this conception of logical hylomorphism is wavering as contemporary non-classical logic, philosophy of logic and psychology of reasoning delve deeply into the problem of reasoning. Given the instability of the form-content distinction, the non-eliminability of material validity, and the robust “content effect” in actual human reasoning, it is reasonable to rethink the role of “formality” and “logical words” in the study of logic from a contemporary multidisciplinary perspective.

Rooted in the unique linguistic and cultural backgrounds of Eastern civilization, Eastern logic exhibits its own distinct characteristics. Both Eastern logic and artificial intelligence (AI) logic are forms of applied logic and experience-based logic. They combine formal truth with material appropriateness and are best understood as a generalized logic wherein classical deductive, non-classical deductive, and non-deductive logic coexist. As a “logic of discovery,” AI logic holds a distinct advantage over Eastern logic. Conversely, Eastern logic is more advanced in its “combination of ‘tool’ (qi 器) and Dao.” The development of Eastern logic offers a key implication for AI logic: a cross-cultural research methodology that requires apprehending a system of thought in its original state by proceeding from its native cultural context. This entails adopting the principle of “grasping the original form” over the conventional method of “interpreting the East by the West.” The nascent field of AI logic can draw intellectual nourishment from the wisdom of ancient Eastern logic, and contemporary explorations of Eastern logic can, in turn, contribute to the advancement of AI logic.

Over the past 70 years since the founding of the People’s Republic of China, there have been several significant discussions in the field of logic, all directly or indirectly related to formal logic. While the concept of formal logic is foundational in the study of logic, many new logical theories have justified their legitimacy by adopting strategies that negate or challenge formal logic. However, in evaluating whether a new theory is innovative or progressive in logic, the critical criterion is not its method of self-justification but whether it adheres to the intrinsic mechanisms of logic. Logic as a discipline has specific research objects and methods, and formal logic is the very foundation of logic.