Jun-shi Sun

Abstract: This paper, building upon the "Dual-Mechanism Model" proposed in Content-Consistent Logic: The Irreplaceability of Traditional Logic in Natural Language Inference (Sun, 2026), further addresses relational reasoning and generalized quantifier reasoning in natural language. It argues that traditional logic is not inherently incapable of handling relations, but rather has not yet established a mechanism for relational deduction and inheritance suited to natural language. Although modern first-order logic can formalize relational structures through variables and quantifiers, its core objective is truth-preservation rather than content-coherent deduction in natural language. Consequently, it cannot replace the innate reasoning mechanisms of natural language itself. This paper proposes that relational reasoning in natural language fundamentally still depends on predicate inheritance within conceptual subordination structures. Through principles such as concept extension, quantifier internalization, relation binarization, the single-step subordination rule, logical descent, and logical ascent, many relational inferences can be reduced back to conceptual reasoning forms in traditional logic. On this basis, the paper further examines how generalized quantifiers (e.g., "most," "almost all," "many," "few") are constrained and mapped in natural language, arguing that their essence is not truth-functional computation in the modern logical sense, but rather content-consistent mapping within a determined domain. The paper systematically analyzes the seven types of generalized quantifier inference examples presented by Zhou (2019), demonstrating that natural language can accomplish complex relational reasoning through conceptual hierarchies, quantifier specification, scope restriction, and descent/ascent logical mechanisms, without relying on higher-order formalization systems in modern logic. The paper further points out that several valid syllogistic forms requiring reduction in traditional syllogistic can be directly supported by descent and ascent inheritance principles at the conceptual level, thus laying the groundwork for a future comprehensive replacement of reduction techniques. This paper maintains that the core objective of natural language logic is not abstract truth-value computation, but the consistency-preservation of conceptual content. Logic is primarily a system of content deduction, rather than a binary truth-functional calculus. The foundational status of traditional logic in natural language inference has not been genuinely superseded by modern logic.

The visual world appears unified, stable, and continuous despite rapid changes in eye position. How this is accomplished has puzzled psychologists for over a century. One possibility is that visual information from successive eye fixations is fused in memory according to environmental or spatiotopic coordinates. Evidence supporting this hypothesis was provided by Davidson, Fox, and Dick (1973). They presented a letter array in one fixation and a mask at one letter position in a subsequent fixation and found that the mask inhibited report of the letter that shared its retinal coordinates but appeared to occupy the same position as the letter that shared its spatial coordinates. This suggests the existence of a retinotopic visual persistence at which transsaccadic masking occurs and a spatiotopic visual persistence at which transsaccadic integration, or fusion, occurs. Using a similar procedure, we found retinotopic masking and retinotopic integration: The mask interfered with the letter that shared its retinal coordinates, but also appeared to cover that letter. In another experiment, instead of a mask we presented a bar marker over one letter position, and subjects reported the letter that appeared underneath the bar; subjects usually reported the letter with the same retinal coordinates as the bar, again suggesting retinotopic rather than spatiotopic integration across saccades. In Experiment 3 a bar marker was again presented over one letter position, but in addition a visual landmark was presented after the saccade so that subjects could localize the bar's spatial position; subjects still reported that the letter that shared the bar's retinal coordinates appeared to be under it, but they were also able to accurately specify the bar's spatial position. This ability could have been based on retinal information (the visual landmark) present in the second fixation only, however, rather than spatiotopic visual persistence. Because such a visual landmark was present in the Davidson et al. (1973) experiments, we conclude that their findings can be explained solely in retinotopic terms and provide no convincing evidence for spatiotopic visual persistence. But the exposure parameters that Davidson et al. (1973) and we used were biased in favor of retinotopic, rather than spatiotopic, coding: The stimuli were presented very briefly just before a saccadic eye movement, and subjects are poor at spatially localizing stimuli under these conditions. Thus, in Experiment 4 we presented the letter array about 200 ms before the saccade; then, subjects reported that the letter with the same spatial coordinates as the bar appeared under it. This result demonstrates the existence of a spatiotopic memory that combines information from successive fixations, but it does not show whether this memory operates by means of spatiotopic visual fusion. To determine this, in the last experiment 4 randomly chosen dots from a 3 x 3 dot matrix were presented in one fixation, and 4 different dots from the matrix were presented in a second fixation. Subjects reported the location of the missing dot. When the first display was presented just before the saccade (as in Experiments 1-3), subjects accurately specified the missing dot location when the dots were presented to the same region of the retina but not when they were presented in the same place in space. When the first display was presented well before the saccade (as in Experiment 4), subjects performed poorly regardless of retinal or spatial overlap. These results indicate the existence of a short-lived retinotopic visual persistence but provide no support for a spatiotopic visual persistence capable of fusing the contents of successive fixations. We conclude that transsaccadic integration depends instead on an abstract memory that accumulates position and identity information about the contents of successive fixations.

The categorical syllogism, as the core of traditional formal logic, has long been criticized for its inability to handle relational reasoning, leading many to argue that it should be replaced by first-order logic. This paper argues that this criticism misunderstands the nature of traditional logic. Traditional logic is grounded in "content consistency" rather than "truth preservation," and its core principle—Dictum de Omni et Nullo—was never inherently restricted to property-based reasoning; its perceived limitations arose from a historical contraction in its mode of expression. The central contribution of this paper is the proposal of a "dual-mechanism model" for natural language logic. First, an extensional reasoning mechanism, based on the subordination relations of concept extensions, is developed. This mechanism extends the predicate in the Dictum de Omni et Nullo from a single concept to a "compound predicate," thereby enabling it to handle reasoning involving properties, relations, and their combinations. Second, an intensional reasoning mechanism, based on the satisfaction of a concept's defining conditions, is introduced. This mechanism systematically addresses relational reasoning, complex property judgments, and object reasoning by verifying whether objects or groups of objects meet the intensional conditions of a concept. Both mechanisms adopt the form of "two premises leading to one conclusion" and are collectively termed the generalized syllogism. Through this model, traditional formal logic is refined and extended, allowing it to comprehensively cover both property-based and relational reasoning in natural language, thereby establishing its independent and irreplaceable status in this domain.