Andrew Schumann

In this paper, we introduce the concept of logemes, a novel framework for reasoning that bridges nontrivial fragments of formal logic and topological spaces. Logemes are defined as logic diagrams that capture logical relationships relevant to specific datasets or problems. Unlike standard symbolic logic, which emphasizes completeness and formal validation within an algebraic framework, logemes focus on pragmatic, nontrivial subsets of inference rules tailored to real-world reasoning tasks. This approach builds on historical tools like logic diagrams (e.g. the square of opposition) while leveraging the combinatorial and topological richness of simplicial complexes. The paper explores the interplay between syntax and semantics through logemes, using topology to compare logical fragments across different systems. By focusing on structural properties rather than syntactic or semantic details, logemes reveal deeper similarities and differences between reasoning patterns, even when derived from distinct logical frameworks. The narrative alternates between bottom-up and top-down approaches: starting with basic components to build complex systems and simplifying complete systems into manageable fragments. Finally, logemes are connected to homotopy types, positioning them as a bridge between reasoning and topology. This unified framework offers a modular, flexible tool for studying logical fragments. By grounding reasoning in the topology of simplicial complexes, logemes provide a novel paradigm for analysing datasets and logical systems.

This paper proposes a phenomenological approach to philosophical logic by reexamining the overlooked yet deeply insightful position of Zaremba in his historical dispute with leading Polish logicians of the early 20th century. Rather than treating this debate as a closed chapter, we argue that Zaremba’s critique remains highly relevant for understanding the limits of formal logic and the need for a more structurally sensitive model of reasoning. His emphasis on the relational and contextual nature of logic challenges the formalist vision of mathematics as a system reducible to axioms. To address this challenge, we introduce a formal mathematical language designed to represent and analyze logemes – the minimal, context-dependent units of logical reasoning. This framework employs simplicial complexes as a topological structure to model how local fragments of reasoning interconnect. Each vertex represents a basic proposition, while higher-dimensional simplices capture the logical relations among them, forming coherent yet flexible substructures. This approach makes it possible to represent interactions among diverse logical systems (such as classical and intuitionistic logic) in a unified, geometrically intuitive manner. By modeling logic not as a unified system but as a dynamic network of interrelated fragments, this work offers a new foundation for philosophical logic – one that is capable of expressing ambiguity, incompleteness, and contextual variation, and that aligns more closely with the actual structure of mathematical and human reasoning. This approach may have a wide and rich range of practical applications in artificial intelligence. It provides a universal representation of databases in the form of logemes, as well as universal models for non-monotonic reasoning. Together, these features make it possible to model key phenomena of consciousness, such as context sensitivity, revision of beliefs, and circularity. By offering a mathematically rigorous framework for non-monotonicity, the approach opens new possibilities for integrating logical, topological, and cognitive structures in AI systems, potentially contributing to more flexible, adaptive, and cognitively plausible models of artificial intelligence.

Knocking on Heaven's Door is the oldest human dream that seems unrealized still. Religious discourse does show the road, but it requires a blind faith in return. In this book logicians try to hear Heaven's Call and to analyze religious discourse. As a result, the notion of religious logic as a part of philosophical logic is introduced. Its tasks are (1) to construct consistent logical systems formalizing religious reasoning that at first sight seems inconsistent (this research is fulfilled within the limits of modal logic, paraconsistent logic and many-valued logic), (2) to carry out an illocutionary analysis of religious discourse (this research is fulfilled in frames of illocutionary logics), and (3) to formalize Ancient and Medieval logical theories used in the theology of an appropriate religion (they could be studied within the limits of unconventional logics, such as non-monotonic logics, non-well-founded logics, etc.).

According to logical psychologism that was popular in the nineteenth century, logic was regarded as a natural ability of human psychology. Consequently, logical competence as a realization of logic knowledge was treated as one of the innate features of human thinking. Nevertheless, within cognitive science, it was experimentally proved that our thinking is not free from cognitive biases, and to the same extent, our reasoning is not free from logical fallacies. Hence, we are forced to consciously clear the thinking of possible distortions to follow logical norms and to realize logical competence thereby. In the paper, it is shown that some cognitive biases are observed even at the level of cellular reactions to the environment and then at the level of animal behavior. Therefore not logic, but cognitive biases are a natural (biological) mechanism of human thinking. So, the problem of defining logical competence arises. In this paper, there are some arguments that logical competence has once appeared as an especial social practice and it has then been developed for a long time before the first treatises on logic.

The interview given by Adam Hlobus (Uladzimir Vyachaslavavich Adamchyk, born September 29, 1958), a Belarusian writer, poet, artist, and publisher. He began publishing poetry in 1981 (in the newspaper Literature and Art and the magazine Maladosts). He is the founder of the Society of Young Writers “Tuteyshiya” (1986–1988). Selected books: Park (poetry, 1988), Loneliness at the Stadium (short stories, 1989), Death Is a Man (1992), Crossroads (1993), Damavikameron (1994), Just Don’t Tell My Mom (1995), Koidanava (1997), New Damavikameron (1998), Post Scriptum (1999), Texts (a collection of all previous books, 2000), Braslav Stigmata (2001), Notebooks (2003), Home (2005), coParticipants (2006), Letters (2006), Fairy Tales (2007), Convolutus (2008), Castle (2008), PLAY.BY (2009), Krutahory Fairy Tales (2010), New Sky (2010), Sayings (2012), Names. Literary Portraits (2013), Fairy Tales for Adults (2013), Portraits (2014), Stories about Minsk and Its Surroundings (2015), Reverse Perspective (2016), Family (2017), Capital Fairy Tales (2018), Features (2019), Angel (2021), Snowflake (2022), Our Neighbor Karatkevich (2025).

The interview given by Gershon Trestman (born July 29, 1947, Minsk), a Russian-language Belarusian and Israeli poet, prose writer, publicist, and playwright. He is a member of the Union of Writers of Israel, the Commonwealth of Russian-Speaking Writers of Israel “Stolitsa,” and the International Federation of Russian Writers. His work has been recognized with the Yu. Stern and Yu. Nagibin awards, as well as a gold medal for “outstanding achievements in literature and the arts” from the California Academy of Sciences. Selected works: The One Who Crossed the River (Tel Aviv, 1996); Golem, or Faust’s Curse (Moscow, 2007); A Small Country with a Great History (Israel, 2008, foreword by Avigdor Lieberman); The Great History of a Small Country (Israel, 2011); The Scroll of Esther (Jerusalem, 2013); The Land of Olive Guardians (Jerusalem, 2013); The Israeli Knot: The History of the Country – The History of Confrontation (Book-Sefer, 2014); The Land of Olive Guardians (Jerusalem, KKL-JNF, 2014); Job (Minsk, New Wineskins, 2014);... Where There Are No Coordinates. Poems and Epics (Jerusalem, 2017); The Book of Non-Being (Minsk, Logvinov, 2019); Alphabet for Elderly Children (Jerusalem, 2023).

We show that in Kabbalah, the esoteric teaching of Judaism, there were developed ideas of unconventional automata in which operations over characters of the Hebrew alphabet can simulate all real processes producing appropriate strings in accordance with some algorithms. These ideas may be used now in a syllogistic extension of Lindenmayer systems, where we deal also with strings in the Kabbalistic-Leibnizean meaning. This extension is illustrated by the behavior of Physarum polycephalum plasmodia which can implement, first, the Aristotelian syllogistic and, second, a Talmudic syllogistic by qal wa-homer.

In this paper we consider possibilities for applying p-adic valued logic BL to the task of designing an unconventional computer based on the medium of slime mould, the giant amoebozoa that looks for attractants and reaches them by means of propagating complex networks. If it is assumed that at any time step t of propagation the slime mould can discover and reach not more than attractants, then this behaviour can be coded in terms of p-adic numbers. As a result, this behaviour implements some p-adic valued arithmetic circuits and can verify p-adic valued logical propositions

The Orthodox Christian thought is the most modally rigorous way of inferring. The subject of the book is to investigate possibilities of explicating the Orthodox thought from the viewpoint of analytic philosophy and symbolic logic. The claim that Orthodox thinking is just mystic and illogical is not true. The logical culture of Orthodox Christian thinking is unknown and ununderstandable for the West, although its schemata are very influential in Eastern Europe till now (Marxism-Leninism is just one of their possible instances). This thought can be called totalistic or even totalitarian. For this thought any truth or falsity is necessary. As a result, the whole world is presented as logical and nomothetic and there is no place for contingency.