We introduce Aristotle, an AI system that combines formal verification with informal reasoning, achieving gold-medal-equivalent performance on the 2025 International Mathematical Olympiad problems. Aristotle integrates three main components: a Lean proof search system, an informal reasoning system that generates and formalizes lemmas, and a dedicated geometry solver. Our system demonstrates state-of-the-art performance with favorable scaling properties for automated theorem proving.

The ideas that he raised in his study of logical reasoning carried the development of science over the centuries. Any scientific theory's mathematical formalization is one that falls under his idea of Demonstrative Science. T oday, in the era of AI, this title of the fatherhood of logic has a renewed significance . Behind it li es his original idea that human reasoning c ould be studied as a process and that perhaps there exist universal systems of reasoning that underly all human reasoning irrespective of the content of what we are reasoning about . This is a daring idea as it ess entially says that the human mind can study itself and indeed that it has the capacity to unravel its own self. Irrespective of whether this is possible or not, it is a thought that is a prerequisite for the existence and development of Artificial Intellig ence. In this article, we look into Aristotle's work on human thought, his work on reasoning itself but also on how it relates to science and human endeavour more generally, from a modern perspective of Artificial Intelligence and ask if this can help enli ghten our understanding of AI and S cience more generally.

This is an essay about the value of mathematical and symbolic reasoning in the age of AI.

The automation of work, understood as the process by which human labour is replaced by machines, is also a cause for scholarly concern across different disciplines. For some scholars, the large-scale deployment of AI in the workplace amounts to a'Fourth Industrial Revolution' or a'Second Machine Age', threatening to render human work--nay, humankind in its entirety--obsolete [3],[6]. Even despite the potential introduction of a Universal Basic Income (UBI), which could in principle guarantee citizens' livelihood, it is argued that policymakers would still need to safeguard work, since it bears intrinsic value that transcends the instrumental value of a paycheck [8]. AI-driven automation is, hence, largely framed as a threat to be counteracted by law. Nonetheless, the axiological superiority of work as an intrinsically valuable activity and the insistence on its preservation, even if humans' sustenance could be otherwise secured, should not be taken for granted.

Given a raw knowledge in the form of a data table/a decision system, one is facing two possible venues. One, to treat the system as closed, i.e., its universe does not admit new objects, or, to the contrary, its universe is open on admittance of new objects. In particular, one may obtain new objects whose sets of values of features are new to the system. In this case the problem is to assign a decision value to any such new object. This problem is somehow resolved in the rough set theory, e.g., on the basis of similarity of the value set of a new object to value sets of objects already assigned a decision value. It is crucial for online learning when each new object must have a predicted decision value.\ There is a vast literature on various methods for decision prediction for new yet unseen object. The approach we propose is founded in the theory of rough mereology and it requires a theory of sets/concepts, and, we root our theory in classical set theory of Syllogistic within which we recall the theory of parts known as Mereology. Then, we recall our theory of Rough Mereology along with the theory of weight assignment to the Tarski algebra of Mereology.\ This allows us to introduce the notion of a part to a degree. Once we have defined basics of Mereology and rough Mereology, we recall our theory of weight assignment to elements of the Boolean algebra within Mereology and this allows us to define the relation of parts to the degree and we apply this notion in a procedure to select a decision for new yet unseen objects.\ In selecting a plausible candidate which would pass its decision value to the new object, we employ the notion of Vapnik - Chervonenkis dimension in order to select at the first stage the candidate with the largest VC-dimension of the family of its $\varepsilon$-components for some choice of $\varepsilon$.

AlphaGo plays chess and Go in a creative and novel way. It is natural for us to attribute contents to it, such as that it doesn't view being several pawns behind, if it has more board space, as bad. The framework introduced in Cappelen and Dever (2021) provides a way of thinking about the semantics and the metasemantics of AI content: does AlphaGo entertain contents like this, and if so, in virtue of what does a given state of the program mean that particular content? One salient question Cappelen and Dever didn't consider was the possibility of alien content. Alien content is content that is not or cannot be expressed by human beings. It's highly plausible that AlphaGo, or any other sophisticated AI system, expresses alien contents. That this is so, moreover, is plausibly a metasemantic fact: a fact that has to do with how AI comes to entertain content in the first place, one that will heed the vastly different etiology of AI and human content. This chapter explores the question of alien content in AI from a semantic and metasemantic perspective. It lays out the logical space of possible responses to the semantic and metasemantic questions alien content poses, considers whether and how we humans could communicate with entities who express alien content, and points out that getting clear about such questions might be important for more 'applied' issues in the philosophy of AI, such as existential risk and XAI.

The paper addresses the question of whether it is appropriate to talk about `mechanical minds' at all, and whether ChatGPT models can indeed be thought of as realizations of that. Our paper adds a semantic argument to the current debate. The act of human assertion requires the formation of a veridicality judgment. Modification of assertions with modals (John must be at home) and the use of subjective elements (John is obviously at home) indicate that the speaker is manipulating her judgments and, in a cooperative context, intends her epistemic state to be transparent to the addressee. Veridicality judgments are formed on the basis of two components: (i) evidence that relates to reality (exogenous evidence) and (ii) endogenous evidence, such as preferences and private beliefs. `Mechanical minds' lack these two components: (i) they do not relate to reality and (ii) do not have endogenous evidence. Therefore they lack the ability to form a belief about the world and a veridicality judgments altogether. They can only mimic that judgment, but the output is not ground in the very foundations for it.

Solving the AI alignment problem requires having clear, defensible values towards which AI systems can align. Currently, targets for alignment remain underspecified and do not seem to be built from a philosophically robust structure. We begin the discussion of this problem by presenting five core, foundational values, drawn from moral philosophy and built on the requisites for human existence: survival, sustainable intergenerational existence, society, education, and truth. We show that these values not only provide a clearer direction for technical alignment work, but also serve as a framework to highlight threats and opportunities from AI systems to both obtain and sustain these values.

Although modal logic is regarded as a relatively young field, its origins can be traced back to Aristotle, who explored syllogistic reasoning patterns that incorporated modalities. However, in contrast to his utterly successful assertoric syllogistic, Aristotle's examination of modal syllogisms is often viewed as error-prone and controversial, thus receiving less attention from logicians. In the literature, a large body of research on Aristotle's modal syllogistic primarily centers on the possibility of a coherent interpretation of his proposed modal systems grounded by his philosophy on necessity and contingency (see, e.g., [11, 5, 12]). We adopt a more liberal view on Aristotle's modal syllogistic, considering it as a source of inspiration for formalizing natural reasoning patterns involving modalities, rather than scrutinizing the coherence of the original systems. Our approach is encouraged by the fruitful research program of natural logic, which explores "light" logic systems that admit intuitive reasoning patterns in natural languages while balancing expressivity and computational complexity [1, 8]. In particular, various extensions of the assertoric syllogistic have been proposed and studied [8]. In this paper, we propose a systematic study on epistemic syllogistic to initiate our technical investigations of (extensions of) modal syllogistic. The choice for the epistemic modality is intentional for its ubiquitous use in natural languages. Consider the following syllogism: All C are B Some C is known to be A Some B is known to be A Taking the intuitive de re reading, the second premise and the conclusion above can be formalized as x(Cx KAx) and x(Bx KAx) respectively in first-order modal logic (FOML).

There is a recent trend for using the novel Artificial Intelligence ChatGPT chatbox, which provides detailed responses and articulate answers across many domains of knowledge. However, in many cases it returns plausible-sounding but incorrect or inaccurate responses, whereas it does not provide evidence. Therefore, any user has to further search for checking the accuracy of the answer or/and for finding more information about the entities of the response. At the same time there is a high proliferation of RDF Knowledge Graphs (KGs) over any real domain, that offer high quality structured data. For enabling the combination of ChatGPT and RDF KGs, we present a research prototype, called GPToLODS, which is able to enrich any ChatGPT response with more information from hundreds of RDF KGs. In particular, it identifies and annotates each entity of the response with statistics and hyperlinks to LODsyndesis KG (which contains integrated data from 400 RDF KGs and over 412 million entities). In this way, it is feasible to enrich the content of entities and to perform fact checking and validation for the facts of the response at real time.