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Fabien Schang, Jaap Hage, Jan Woleński, Matheus Gabriel Barbosa, Vadim Verenich, Andrea Reichenberger, Andrew Schumann,


Logic and Law: A Matter of Values Behind Content and Form

The Author: Fabien Schang,
This special issue on Logic and Law consists of four research papers and one interview focusing on epistemological reflections on relationships between logic and law, whether in a reductionist or complementary approach. Logic aims to elucidate through formal frameworks, yet it often grapples with the intricate nuances of everyday legal discourse. While law endeavors to delineate permissible conduct within defined jurisdictions, it often encounters challenges stemming from the ambiguity of terms, leading to frequent judicial interpretations and the perception that proliferating exceptions undermines the efficacy of the rule itself.

How Law’s Nature Influences Law’s Logic

The Author: Jaap Hage,
Classical logic is based on an underlying view of the world, according to which there are elementary facts and compound facts, which are logical combinations of these elementary facts. Sentences are true if they correspond to, in last instance, the elementary facts in the world. This world view has no place for rules, which exist as individuals in the world, and which create relations between the most elementary facts. As a result, classical logic is not suitable to deal with rules, and is therefore unsuitable to deal with legal reasoning. A logic that is more suitable should take into account that law is a part of social reality, in particular a part that consists of constructivist facts, and that rules play a central role in law. This article gives a superficial description of how social reality exists and of the place of law and legal rules in it. It uses this description to argue that traditional techniques to reason with and about legal rules provide a better logic for law than classical logic. These techniques can be accommodated in a logic that treats rules as logical individuals.

Legal Reasoning and Logic

The Author: Jan Woleński,
This paper investigates the basis arguments of so-called legal logic and their relation to logic in its standard meaning. There is no doubt that legal arguments belong to logic in the wide sense (sensu largo), but their reduction to schemes of formal logic (logica sensu stricto) is a controversial issue. It can be demonstrated that only some legal arguments fall under explicit rules of formal logic, that is, having a deductive character. Most such reasoning is fallible, and its correctness depends on appealing to extra-logical principles taken from legal norms. For instance, if we say, “If it is permitted more, then it is permitted less” (argumentum a maiori ad minus), we assume that the concepts expressed by the words “more” and “less” are already defined.

Legal Gaps and their Logical Forms

The concept of legal gap is tackled from a number of logical perspectives and semantic methods. After presenting our own goal (Section 1), a first introduction into legal logic refers to Bobbio’s works and his formalization of legal statements (Sections 2 and 3). Then Woleński’s contribution to the area is taken into account through his reference to the distinction between two juridical systems (viz. Common Law vs Civil Law) and the notion of conditional norms (Section 4). The notion of reason is also highlighted in the case of Raz’s legal logic, thereby leading to a future connection with von Wright’s logic of truth and an analogy made with an anti-realist reading of truth-values and norms (Section 5). Our personal contribution is introduced through a reflection on how logic should deal with the logical form of norms (Section 6), before entering a number of crucial definitions and distinctions for the concepts of norm, legal statement, and promulgation (Section 7). The final point is a proposed semantics for legal statements, which is both many-valued and gap-friendly (Section 8). A distinction between a number of requirements for permission and forbiddance leads to a set of non-classical juridical systems in which non-permission and forbiddance are not equivalent with each other any more; this does justice to Woleński’s former distinction between Common Law and Civil Law, also leading ultimately to a non-classical square of legal oppositions in which several legal operators may collapse into other ones (Section 9).

Neural Networks in Legal Theory

The Author: Vadim Verenich,
This article explores the domain of legal analysis and its methodologies, emphasising the significance of generalisation in legal systems. It discusses the process of generalisation in relation to legal concepts and the development of ideal concepts that form the foundation of law. The article examines the role of logical induction and its similarities with semantic generalisation, highlighting their importance in legal decision-making. It also critiques the formal-deductive approach in legal practice and advocates for more adaptable models, incorporating fuzzy logic, non-monotonic defeasible reasoning, and artificial intelligence. The potential application of neural networks, specifically deep learning algorithms, in legal theory is also discussed. The article discusses how neural networks encode legal knowledge in their synaptic connections, while the syllogistic model condenses legal information into axioms. The article also highlights how neural networks assimilate novel experiences and exhibit evolutionary progression, unlike the deductive model of law. Additionally, the article examines the historical and theoretical foundations of jurisprudence that align with the basic principles of neural networks. It delves into the statistical analysis of legal phenomena and theories that view legal development as an evolutionary process. The article then explores Friedrich Hayek’s theory of law as an autonomous self-organising system and its compatibility with neural network models. It concludes by discussing the implications of Hayek’s theory on the role of a lawyer and the precision of neural networks.

Logic Matters – Gender and Diversity, Too

This interview features Andrea Reichenberger. Currently she holds a substitute professorship for history of technology at TUM Technical University of Munich. She is junior research group leader at the Department of Mathematics, University of Siegen, Germany, and leads the research project “Rethinking the History of Mathematics and Physics: Women in Focus.” Reichenberger has held several postdoctoral positions, e.g., at the Center for the History of Women Philosophers and Scientists (HWPS) at Paderborn University (Germany) and in the DFG research project “Thought Experiment, Metaphor, Model” at the Institute for Philosophy I at the Ruhr University Bochum. Between 2019 and 2021, she was a fellow at the University of Paderborn and principal investigator of the research project “Foundational research in mathematical logic – relativity – quantum physics. Case studies on the integration of women philosophers.” Reichenberger has written a book on Émilie du Châtelet (Springer, 2016) and has published many articles in journals, collected editions, and encyclopedias.