The article analyzes the concepts of scientists regarding the understanding of the essence of the concepts of “proof” and “demonstration” and their correlation. The author proves, based on his personal lawyer experience, analysis of judicial practice in civil cases and in the context of studying evidence, arguments and considerations expressed by the participants in the case and evaluated by the court according to his internal conviction that proof and demonstration cannot be identified and regarded as synonyms, as some scientists believe. These are different legal categories, which the author proves, based on the analysis of the features of the demonstration process, in particular, in such a procedure as dispute settlement with the participation of a judge and when considering various categories of cases, in particular, general and simplified claim proceedings. The author analyzed civil procedural legislation, norms of civil substantive branches of law, as well as criminal law and found that in addition to the terms “evidence” and “proof”, they operate with such terms as “reasons”, “reasoning”, “arguments”, “proof”, however, there is a lack of scientific research on these legal categories. The author draws attention to the significant scientific achievements of scientists, where the theory of proof in civil proceedings is formulated and emphasizes that such a theory should now be developed and improved by both scientists and practitioners in order to introduce its basic provisions into civil procedural legislation. Such an approach will provide an opportunity to identify shortcomings in the regulation of certain civil procedures, in particular, the interrogation of participants in the case as witnesses (Article 93 of the Code of Civil Procedure) and to make amendments to the Civil Procedural Code of Ukraine in order to guarantee the protection of violated, unrecognized or disputed rights, freedoms or interests of persons. The distinction between the concepts of «proving» and «proving» provides an opportunity to look at the innovations in the CPC in a different way, where in many cases there is no difference between the provision of evidence to the court as a procedural activity of the participants in the case and the exchange between the parties of arguments, considerations, arguments, in particular, regarding the evidence submitted by the party, its relevance, admissibility, etc., which will have a significant impact on their final assessment by the court in its decision.

The issue examined in this thesis concerns the analysis of the implementation and challenges in applying the reverse burden of proof system in money laundering crimes in Indonesia, using the Law Enforcement Theory and the Proof Theory. The reverse burden of proof system is a special mechanism in criminal procedural law that obliges the defendant to prove that the assets alleged are not derived from criminal acts, as regulated in Articles 77 and 78 of Law Number 8 of 2010 concerning the Prevention and Eradication of Money Laundering Crimes. The method used in this research is normative legal research conducted as an effort to obtain the necessary data related to the problem. The data used consists of secondary data and tertiary legal materials. In addition, primary data is also used to support the secondary legal materials. Data analysis is carried out using qualitative juridical analysis methods. The research results show that the implementation of the reverse burden of proof system has a clear legal basis and is limited and balanced, where the Public Prosecutor remains obligated to prove the elements of the crime of money laundering, while the defendant is burdened with the obligation to explain the origin of their wealth. There are several rulings where judges have given defendants the opportunity to prove ownership of the wealth, but based on the evidence submitted at trial, the panel of judges concluded that the defendants could not prove that the wealth was obtained through lawful acts or did not originate from a crime or offense. This construction does not eliminate the presumption of innocence but serves as a special instrument to strengthen evidence in complex cases. However, its implementation still faces various challenges, including potential conflicts with human rights protection principles, the absence of uniform technical guidelines, disparities in judicial interpretation, and limited capacity of officials in financial investigations. Therefore, strengthening technical regulations and enhancing law enforcement capacity are necessary to ensure this system operates optimally and aligns with the principles of the rule of law.

The article is devoted to a comprehensive analysis of the evolution of political advertising genres in the context of pervasive digitalization and the development of digital platforms. The transformation of traditional formats (printed advertising, radio, television) under the influence of the digital media space is considered, and the characteristic features of new genre forms that have become widespread in the online environment are identified. Particular attention is paid to such viral formats as political memes and their semiotic transformation from political posters, short videos on the TikTok platform with an analysis of their structural features and mechanisms of influence on the youth audience, as well as interactive content and user-generated content. Scientific publications that initiated the solution of the raised problem are analyzed, and the relevance of further research on the specifics of genre transformation, mechanisms of influence, and ethical consequences of using new digital genres of political advertising is substantiated. The aim of the article is to study this transformation, identify genre features, mechanisms of influence, and ethical consequences of new viral formats of political communication in the online environment. Based on the analysis of theoretical approaches (dual-coding theory, network effects theory, social constructivism theory, incongruity theory of humor, affect theory, STEPPS model, social learning theory, framing theory, information overload theory, attention theory, musical influence theory, narrative persuasion theory, audience segmentation theory, political leader image theory, message simplification theory, filter bubble theory, social proof theory, imitation theory), the peculiarities of the functioning and influence of new digital genres of political advertising are revealed.

Cambridge University Press has recently published my book, "Proof Theory and Logic Programming: Computation as Proof Search" (December 2025). A preprint of the full text is available for download [1].

Welcome to the first SIGLOG News issue of 2026! This is a period dense of activities for all of us, both because it is a moment in which many submission deadlines fall and because many of us are busy in their teaching duties. For this reason, also this issue comes without any technical column. To try and improve the vitality of this publication, from the next issue we shall change some of the column editors, that have so far contributed to the quality and interest of SIGLOG News. Indeed, the Executive Committee and myself has agreed that column editors are nominated for three years, with the possibility of renewal. In this way, SIGLOG News will be more and more a place where our community can express and present its research interests. Let me also take this occasion to encourage all of you to contribute, by also directly contacting the column editors and proposing a possible column. Nevertheless, this issue has some interesting content: — First of all, we have the letter of the SIGLOG Chair Catuscia Palamidessi describing the actual situation of SIGLOG. — Second, Dale Miller introduces its recent book "Proof Theory and Logic Programming: Computation as Proof Search" , published last December by Cambridge University Press. — Finally, we wrap up this number with the latest issue of SIGLOG Monthly, prepared by Elli Anastasiadi. Enjoy reading!

Abstract We introduce a geometric model of shallow multiplicative exponential linear logic (MELL) using the Hilbert scheme. Building on previous work interpreting multiplicative linear logic (MLL) proofs as systems of linear equations, we show that shallow MELL proofs can be modelled by locally projective schemes. The key insight is that while MLL proofs correspond to equations between formulas, the exponential fragment of shallow proofs corresponds to equations between these equations. We prove that the model is invariant under cut-elimination by constructing explicit isomorphisms between the schemes associated with proofs related by cut-reduction steps. A key technical tool is the interpretation of the exponential modality using the Hilbert scheme, which parameterises closed subschemes of projective space. We demonstrate the model through detailed examples, including an analysis of Church numerals that reveals how the Hilbert scheme captures the geometric content of promoted formulas. This work establishes new connections between proof theory and algebraic geometry, suggesting broader relationships between computation and scheme theory.

In her seminal article ‘Proper Classes’, Penelope Maddy introduced a novel theory of classes validating the naïve comprehension rules. The theory is based on a step-by-step construction of the extension and anti-extension of the membership predicate, which mirrors Kripke’s construction of the extension and anti-extension of the truth predicate. Maddy’s theory has been criticized by Øystein Linnebo for its ‘rampant indeterminacy’ and for making identity among classes too fine-grained. In this paper, I present a theory of classes which, while building on Maddy’s theory, avoids its rampant indeterminacy and allows for identity among classes to be suitably coarsegrained. I begin by presenting a bilateral natural deduction system for Maddy’s theory, which improves on her axiomatization in several respects. I then go on to show how to avoid the rampant indeterminacy by using supervaluational schemes in the construction of the extension and anti-extension of the membership predicate and how to augment the proof theory with corresponding, motivated rules. It turns out that whilst a van Fraassen-style supervaluational scheme suffices to avoid the basic problem of rampant indeterminacy, a supervaluational scheme based on maximally consistent extensions is needed for a proper treatment of identity.

General Background: Judicial conviction is a central component of Indonesia’s criminal justice system, which adopts the negative proof theory under Article 183 KUHAP. Specific Background: Growing discrepancies between judicial conviction and legally valid evidence, illustrated by Surabaya District Court Decision Number 454/Pid.B/2024/PN.Sby, have raised concerns regarding doctrinal consistency and judicial practice. Knowledge Gap: Limited studies integrate normative analysis, case-based evaluation, and Islamic legal perspectives to define the boundaries of judicial conviction. Aims: This study examines the relevance and limitations of judicial conviction within the negative proof model and assesses its application in the referenced court decision, complemented by Islamic jurisprudential insights. Results: Findings indicate that although the negative proof system remains normatively sound, judicial practice reveals deviations when conviction becomes overly subjective and insufficiently grounded in evidence; Islamic law emphasizes that judicial belief must be based on proof and moral accountability. Novelty: This research offers an integrative framework combining normative doctrine, case analysis, and Islamic legal principles to reinterpret the objective limits of judicial conviction. Implications: Strengthening objective standards, judicial integrity, and ethical safeguards is necessary to ensure proper application of Article 183 KUHAP and to restore public trust in judicial institutions. Highlights: The negative proof system requires judicial conviction to be firmly grounded in valid evidence. The Surabaya court case illustrates how subjective conviction can distort legal reasoning. Islamic legal principles reinforce the need for moral accountability in judicial decision-making. Keywords: Judicial Conviction, Negative Proof Theory, Article 183 KUHAP, Judicial Integrity, Islamic Legal Perspective

The paper “Tautology elimination, cut elimination, and S5” published in this journal presents a novel method for establishing by proof analysis the admissibility of the rule of tautology elimination for certain sequent calculi. Since tautology elimination will typically imply the admissibility of cut, the method promises a new path to show the admissibility of cut for cut-free calculi on which the standard techniques within structural proof theory seem inapplicable. This paper shows that the method as presented involves an error.

Abstract The topic of this thesis lies in the intersection between proof theory and algebraic logic. The main object of discussion, constructive reasoning, was introduced at the beginning of the twentieth century by Brouwer, who followed Kant’s explanation of human intuition of spacial forms and time points: these are constructed step by step in a finite process by certain rules, mimicking constructions with straightedge and compass and the construction of natural numbers, respectively. The aim of the present thesis is to show how classical reasoning, which admits some forms of indirect reasoning, can be made more constructive. The central tool that we are using are induction principles, methods that capture infinite collections of objects by considering their process of generation instead of the whole class. We start by studying the interplay between certain structures that satisfy induction and the calculi for some non-classical logics. We then use inductive methods to prove a few conservation theorems, which contribute to answering the question of which parts of classical logic and mathematics can be made constructive. Abstract prepared by Giulio Fellin E-mail : giulio.fellin@univr.it URL : https://researchportal.helsinki.fi/en/publications/constructivisation-through-induction-and-conservation

Abstract Hegel indicates throughout his writings that the claims most pivotal to his system of philosophical science receive their proof only in logic itself. And yet, Hegel has surprisingly little to say in either the Encyclopaedia Logic or the Science of Logic itself about what he means by ‘proof’ or what sort of proof procedure it is that he thinks is suited to meet such a demand. In this paper, I develop an account of the proof procedure at work in the Logic by considering Hegel’s treatment of the traditional proofs of God’s existence (specifically, the ontological and the cosmological arguments) that he offers in the logical writings and in his Religionsphilosophie. I develop this account through the speculative reconstruction of the traditional arguments of natural theology that Hegel offers in his 1827 Lectures on the Philosophy of Religion and the 1829 Lectures on the Proofs of the Existence of God where, I argue, these arguments are divested of their syllogistic form and reformulated on the model of conceptual mediation. In the end, I explain how this account of the Logic ’s proof procedure sheds light on two lingering interpretive issues in Hegel’s metaphysics: its relationship to the ontological argument and its solution to ‘the problem of beginning’.

This study explores how female Lebanese micro-influencers are redefining jewelry marketing by shifting from celebrity endorsements to more accessible, community-driven campaigns on Instagram. Using the cases of Lynyer, Joanna Dahdah Fine Jewellery, and MBLSHD, the research highlights how women influencers contribute to sustainable branding practices by fostering authenticity, trust, and inclusive consumer engagement. Anchored in Emotional Branding, Parasocial Interaction, and Social Proof theories, the analysis emphasizes the gendered dimension of influence, showing how women leverage personal narratives and peer connections to humanize jewelry and integrate it into everyday life. Findings reveal that female micro-influencers not only democratize jewelry marketing but also align with SDG 5 (Gender Equality) and SDG 8 (Decent Work & Economic Growth), as they enable female entrepreneurship, reshape luxury consumption, and build long-term, trust-based relationships with consumers. This positions women not merely as endorsers but as cultural actors driving both market accessibility and social change.

Consumers increasingly make offline decisions based on online information, often relying on other users’ opinions shared on social media, with hashtags functioning as a form of electronic word of mouth (e-WOM) that amplifies brand messages and shapes audience engagement. This study aims to analyze how the hashtag #TimPakeTangan was utilized as e-WOM in Payakumbuah’s marketing strategy on Twitter. Payakumbuah, a Padang restaurant owned by Arief Muhammad, collaborated with Azizi from JKT48 to popularize the hashtag and enhance brand visibility. Drawing upon Social Proof Theory, this research employs a quantitative approach using Social Network Analysis (SNA) to examine online interactions and network dynamics. Data were collected from Twitter posts containing #TimPakeTangan between January 14 and 16, 2023, and analyzed using Netlytic and Gephi 0.9.7. The analysis identified 3,700 nodes and 5,042 edges, revealing @officialjkt48 as the central actor generating high engagement, while @jeon_sunghye and @a_zeejkt48 played active roles in disseminating the hashtag through replies, retweets, and original posts. The findings indicate that collaborations with influential social media figures significantly enhance e-WOM effectiveness and network reach. Theoretically, this research contributes to understanding how social proof operates within digital communication networks, while practically, it demonstrates how strategic hashtag campaigns and influencer collaborations can strengthen brand awareness and consumer engagement in social media marketing.

This study investigates the impact of Social Media Influencers (SMIs) on the purchasing behavior of Generation Z Filipino consumers, emphasizing the role of influencer attributes in fostering parasocial relationships (PSRs) that ultimately drive online shopping decisions. In the context of the Philippines’ rapidly evolving e-commerce landscape and digitally native Generation Z population, this research explores how nano, micro-, and macro-influencers influence consumer behavior through strategic content and emotional engagement. Grounded in David Chaffey’s Social Media Marketing Theory, Parasocial Interaction Theory, Source Credibility Theory, Source Attractiveness Model, and Social Proof Theory, the study provides a multi-theoretical framework to analyze consumer-influencer dynamics. A quantitative-descriptive approach was used, surveying 380 Generation Z respondents in San Fernando, La Union, through a structured and validated questionnaire. Data were analyzed using descriptive statistics, the Mann-Whitney U test, and Spearman’s rho correlation. Findings reveal that nano-influencers (with 0–10,000 followers) are particularly effective in building trust and emotional connection, significantly strengthening PSRs. Key attributes such as authenticity, content style, perceived fit, and popularity were found to contribute to stronger PSRs and positively influence purchasing intent. Gender differences were observed in emotional engagement, with female respondents demonstrating higher PSR levels, although purchasing behavior was not significantly different across genders. The study concludes that Generation Z consumers value influencers who are relatable, emotionally resonant, and aligned with their values. PSRs play a critical role in shaping buying behavior, making influencer partnerships a powerful strategy in digital marketing. The study recommends that brands collaborate with nano-influencers who exhibit high credibility and emotional appeal to achieve lasting consumer engagement. This research contributes to existing literature by contextualizing influencer marketing within Southeast Asia. It offers practical insights for marketers seeking to optimize strategies for Generation Z in the post-pandemic digital economy.

Abstract Charles Dacre Parsons passed away on April 19, 2024, aged 91. In this obituary, four of his PhD students and one colleague and collaborator discuss, in an order (roughly) determined by the development of Parsons’s career, his engagement with proof theory; Quine; Kant; Brouwer and Gödel; and mathematical structuralism.

The notion of trust is a major player, in many epistemic and computational contexts. Such notion appears especially relevant in all those situations where verification or evaluation of knowledge is missing, not reachable or non-existent, and agents must rely on information received by others. This includes cases where expert knowers may not yet be able to ground their claims, and the public has to build an opinion by considering the dynamic of the information exchange. Formal logic approaches to this aim have been increasingly important and diverse in the last decades. A natural and important extension of such multi-agent contexts is where epistemic acts are performed under uncertainty, at several levels: the claims of the agents may be graded; information may reach agents with a certain degree of probability; and the degree of acceptance or rejection of the information received may not be binary. We present a multi-agent logic of negative trust applied to uncertain judgements. We offer a proof theory and a relational semantics for which standard soundness and completeness results hold.

Formal theories of arithmetic have traditionally been based on either classical or intuitionistic logic, leading to the development of Peano and Heyting arithmetic, respectively. We propose to use $μ$MALL as a formal theory of arithmetic based on linear logic. This formal system is presented as a sequent calculus proof system that extends the standard proof system for multiplicative-additive linear logic (MALL) with the addition of the logical connectives universal and existential quantifiers (first-order quantifiers), term equality and non-equality, and the least and greatest fixed point operators. We first demonstrate how functions defined using $μ$MALL relational specifications can be computed using a simple proof search algorithm. By incorporating weakening and contraction into $μ$MALL, we obtain $μ$LK+, a natural candidate for a classical sequent calculus for arithmetic. While important proof theory results are still lacking for $μ$LK+ (including cut-elimination and the completeness of focusing), we prove that $μ$LK+ is consistent and that it contains Peano arithmetic. We also prove some conservativity results regarding $μ$LK+ over $μ$MALL.27 pages

Abstract Explanations, and in particular explanations which provide the reasons why their conclusion is true, are a central object in a range of fields. On the one hand, there is a long and illustrious philosophical tradition, which starts from Aristotle, and passes through scholars such as Leibniz, Bolzano and Frege, that give pride of place to this type of explanation, and is rich with brilliant and profound intuitions. Recently, Poggiolesi [25] has formalized ideas coming from this tradition using logical tools of proof theory. On the other hand, recent work has focused on Boolean circuits that compile some common machine learning classifiers and have the same input-output behavior. In this framework, Darwiche and Hirth [7] have proposed a theory for unveiling the reasons behind the decisions made by Boolean classifiers, and they have studied their theoretical implications. In this paper, we uncover the deep links behind these two trends, demonstrating that the proof-theoretic tools introduced by Poggiolesi provide reasons for decisions, in the sense of Darwiche and Hirth [7]. We discuss the conceptual as well as the technical significance of this result.

Rapid technological advancements have brought convenience to various fields, including healthcare. Osteoarthritis (OA) is a chronic degenerative joint disease that often affects the knees and hips, particularly in the elderly, and is a major cause of pain, joint dysfunction, and reduced quality of life. The prevalence of OA increases with age, with risk factors such as obesity, excessive activity, and muscle weakness. Early and accurate diagnosis is essential for appropriate treatment. This study aims to develop a diagnostic system for inflammatory arthritis, specifically osteoarthritis, using the Dempster-Shafer method. This method was chosen because of its ability to combine various evidence and expert beliefs to produce a more accurate diagnosis. By utilizing mathematical proof theory, this system is expected to assist medical personnel in detecting OA symptoms more efficiently. The research findings are expected to contribute to the healthcare sector, particularly in improving the accuracy of osteoarthritis diagnosis, allowing for earlier and more appropriate treatment. This system can also be a supporting tool for doctors and patients in understanding joint health conditions.

After the adoption of the Code of Administrative Procedure, ideas about the revival of the principle of objective truth are increasingly being heard in the Russian procedural literature. Some authors even suggest extending this principle not only to administrative justice, but also according to civil cases. Objective truth is often associated with the justice of a judicial decision (fairness), and the possibility of a fair resolution of a dispute is questioned if this high and extremely strict ideal of judicial evidence is not achieved. This article attempts to critically comprehend the philosophical, methodological and scientific foundations of the principle of objective (material) truth in modern conditions of the development of procedural legislation and the practice of its application, as well as legal doctrine. As a result of the analysis of theoretical, ontological, epistemological, procedural and legal grounds, the author comes to the conclusion about the scientific inconsistency of the concept of objective truth in modern civil court proceedings, even in administrative justice, and the predicted utilitarian and practical consequences of the reanimation of the principle of objective truth in civil proceedings, seem to the author quite dangerous for the standard of proper judicial procedure. The category of objective truth is currently not only unreasonable, but also redundant. The practically significant goals and objectives of the civil judicial process can, accordingly, be achieved and implemented without focusing on the objective truth. Objective truth carries the risk of eliminating the adversarial nature and inverting the essence and objectives of certain types of procedural forms involving judicial activity in the field of evidence (for example, administrative justice). Taking into account the constructivist theory of proof, in addition to critical theses, the article also offers positive conclusions – a shift in assessment from the truth or falsity of a conclusion about a fact to an assessment of the relevance of interpreting the factual circumstances of a legitimized social conflict to the rules of legal argumentation and legal dogma.