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According to the traditional view, the following incompatibility holds true: in reasoning, either there is warrant (certainty) or there is novelty. If there is warrant, there is not novelty: that would be the case of deductive reasoning. If there is novelty, there is not warrant: that would be the case of inductive reasoning. Causal reasoning would belong to the second group because there is novelty and, therefore, there is not warrant in it. I argue that this is false: reasoning may have novelty and, nevertheless, be a deductive one. That is precisely what happens in (some) causal reasoning. And I will develop the following line of argumentation: one thing is to warrant that some state of affairs exists and other thing is to warrant that warrant. So we may have correct deductive reasoning without having certainty of that correction, like in some cases of causal reasoning.

Current advances in Artificial Intelligence (AI) and Machine Learning have achieved unprecedented impact across research communities and industry. Nevertheless, concerns around trust, safety, interpretability and accountability of AI were raised by influential thinkers. Many identified the need for well-founded knowledge representation and reasoning to be integrated with deep learning and for sound explainability. Neurosymbolic computing has been an active area of research for many years seeking to bring together robust learning in neural networks with reasoning and explainability by offering symbolic representations for neural models. In this paper, we relate recent and early research in neurosymbolic AI with the objective of identifying the most important ingredients of neurosymbolic AI systems. We focus on research that integrates in a principled way neural network-based learning with symbolic knowledge representation and logical reasoning. Finally, this review identifies promising directions and challenges for the next decade of AI research from the perspective of neurosymbolic computing, commonsense reasoning and causal explanation.

This article argues that the scope of the neutrality duties of non-assistance and prevention allows for an exception – a carve-out for assistance given to the victim State of an armed attack. Rather than weighing in on debates as to whether current State practice accepted as law suffices to establish this rule inductively, the article offers a different approach to grounding the argument for this exception in the methodology of the sources of international law, which thus far has been underexplored. The central argument of the article is that the exception or carve-out—and its contours—deductively flows from the structure of international law of peace and security and, in particular, the victim State's right to self-defence. The purpose of that right—enabling the effective termination of the armed attack—must not be undermined through prohibitions of military assistance and duties of prevention. These considerations define the scope of neutrality duties as revealed through systemic treaty interpretation. Such deductive reasoning equally determines the scope of customary neutrality duties, whether discerning that scope is framed as systemic interpretation or as identification of custom.

The typicality effect describes a phenomenon whereby a typical item is easier to be judged as a member of a category than are atypical items. This effect has been intensively studied in the context of category verification tasks. The present study further investigated the typicality effect using our newly developed category-based deductive reasoning task. Subjects were required to judge whether an incoming stimulus had the properties described in the premise presented before. The stimuli were either typical or atypical members of four target semantic categories or were non-target stimuli. According to the ERP results, three phases were needed to determine whether the object has the property associated with the category in the premise. First, significant amplitude differences were seen between typical and atypical items at N1, which suggested that attention processing was influenced by the expectation in this up-to-down (deductive) process. The premise automatically induced the expectation of the prototype of one concept, i.e. the expectation for the prototype of birds was induced when the premise was “Birds possess the property C”. Typical items (e.g., sparrow) were more similar to the prototype; hence, they were easier to be matched with the prototype induced by the premise than were atypical items (e.g., ostrich). Additionally, there was a dissociation between typical and atypical items at P2, which suggested that the participants' early detection of an item's category membership was influenced by the typicality. Thirdly, N400 effect is related to the process of semantic processes and determining whether the object has the property associated with the category in the premise. N400 mean amplitudes during the 300-500 ms epoch were significantly greater for non-target members than for target members, while words of lower typicality (atypical) evoked greater N400 amplitudes during the 350-450 ms epoch than did words of higher typicality (typical).

Conceptual advances are critical to the vitality of the marketing discipline, yet recent writings suggest that conceptual advancement in the field is slowing. The author addresses this issue by developing a framework for thinking about conceptualization in marketing. A definition of conceptualization is followed by a typology of types of conceptual contributions. The types of conceptual contributions, their similarities and differences, and their importance to the field are described. Thinking skills linked to various types of conceptual contributions are also described, as are the use of tools that can facilitate these skills. The article concludes with a set of recommendations for advancing conceptualization in our field in the years to come.

To be rational is to be able to reason. Thirty years ago psychologists believed that human reasoning depended on formal rules of inference akin to those of a logical calculus. This hypothesis ran into difficulties, which led to an alternative view: reasoning depends on envisaging the possibilities consistent with the starting point—a perception of the world, a set of assertions, a memory, or some mixture of them. We construct mental models of each distinct possibility and derive a conclusion from them. The theory predicts systematic errors in our reasoning, and the evidence corroborates this prediction. Yet, our ability to use counterexamples to refute invalid inferences provides a foundation for rationality. On this account, reasoning is a simulation of the world fleshed out with our knowledge, not a formal rearrangement of the logical skeletons of sentences.

•Deductive and probabilistic reasoning rely on different neurocognitive processes.•Probabilistic reasoning depends on the retrieval of prior knowledge.•Deductive reasoning depends on spatial representations and processes.•People can inhibit their prior knowledge to reason deductively. Reasoning is a process of inference from given premises to new conclusions. Deductive reasoning is truth-preserving and conclusions can only be either true or false. Probabilistic reasoning is based on degrees of belief and conclusions can be more or less likely. While deductive reasoning requires people to focus on the logical structure of the inference and ignore its content, probabilistic reasoning requires the retrieval of prior knowledge from memory. Recently, however, some researchers have denied that deductive reasoning is a faculty of the human mind. What looks like deductive inference might actually also be probabilistic inference, only with extreme probabilities. We tested this assumption in an fMRI experiment with two groups of participants: one group was instructed to reason deductively, the other received probabilistic instructions. They could freely choose between a binary and a graded response to each problem. The conditional probability and the logical validity of the inferences were systematically varied. Results show that prior knowledge was only used in the probabilistic reasoning group. These participants gave graded responses more often than those in the deductive reasoning group and their reasoning was accompanied by activations in the hippocampus. Participants in the deductive group mostly gave binary responses and their reasoning was accompanied by activations in the anterior cingulate cortex, inferior frontal cortex, and parietal regions. These findings show that (1) deductive and probabilistic reasoning rely on different neurocognitive processes, (2) people can suppress their prior knowledge to reason deductively, and (3) not all inferences can be reduced to probabilistic reasoning.

Purpose Aiming to resolve cross-cultural paradoxes in combining artificial intelligence (AI) with human intelligence (HI) for international humanitarian logistics, this paper aims to adopt an unorthodox Yin–Yang dialectic approach to address how AI–HI interactions can be interpreted as a sophisticated cross-cultural knowledge creation (KC) system that enables more effective decision-making for providing humanitarian relief across borders. Design/methodology/approach This paper is conceptual and pragmatic in nature, whereas its structure design follows the requirements of a real impact study. Findings Based on experimental information and logical reasoning, the authors first identify three critical cross-cultural challenges in AI–HI collaboration: paradoxes of building a cross-cultural KC system, paradoxes of integrative AI and HI in moral judgement and paradoxes of processing moral-related information with emotions in AI–HI collaboration. Then applying the Yin–Yang dialectic to interpret Klir’s epistemological frame (1993), the authors propose an unconventional stratified system of cross-cultural KC for understanding integrative AI–HI decision-making for humanitarian logistics across cultures. Practical implications This paper aids not only in deeply understanding complex issues stemming from human emotions and cultural cognitions in the context of cross-border humanitarian logistics, but also equips culturally-diverse stakeholders to effectively navigate these challenges and their potential ramifications. It enhances the decision-making process and optimizes the synergy between AI and HI for cross-cultural humanitarian logistics. Originality/value The originality lies in the use of a cognitive methodology of the Yin–Yang dialectic to metaphorize the dynamic genesis of integrative AI-HI KC for international humanitarian logistics. Based on system science and knowledge management, this paper applies game theory, multi-objective optimization and Markov decision process to operationalize the conceptual framework in the context of cross-cultural humanitarian logistics.

The dual strategy model proposes that people use one of two potential ways of processing information when making inferences. The statistical strategy generates a rapid probabilistic estimate based on associative access to a wide array of information, while the counterexample strategy uses a more focused representation, allowing for a search for potential counterexamples. In the following studies, we explore the hypothesis that individual differences in strategy use are related to the ability to make rapid intuitive logical judgments. In Study 1, we show that this is the case for rapid judgments requiring a distinction between simple logical form and for a novel form of judgment, the ability to identify inferences that are not linked to their premises (non sequiturs). In Study 2, we show that strategy use is related to the ability to make the kinds of rapid logical judgments previously examined over and above contributions of working memory capacity. Study 3 shows that strategy use explains individual variability in rapid logical responding with belief-biased inferences over and above the contribution of IQ. The results of Studies 2 and 3 indicate that under severe time constraint cognitive capacity is a very poor predictor of reasoning, while strategy use becomes a stronger predictor. These results extend the notion that people can make rapid intuitive “logical” judgments while highlighting the importance of strategy use as a key individual difference variable.

Human reasoning has been characterized as often biased, heuristic, and illogical. In this article, I consider recent findings establishing that, despite the widespread bias and logical errors, people at least implicitly detect that their heuristic response conflicts with traditional normative considerations. I propose that this conflict sensitivity calls for the postulation of logical and probabilistic knowledge that is intuitive and that is activated automatically when people engage in a reasoning task. I sketch the basic characteristics of these intuitions and point to implications for ongoing debates in the field.