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Although conventional logical systems based on logical calculi have been successfully used in mathematics and beyond, they have definite limitations that restrict their application in many cases. For instance, the principal condition for…
This essay recounts my personal journey towards a deeper understanding of the mathematical foundations of algorithmic music composition. I do not spend much time on specific mathematical algorithms used by composers; rather, I focus on…
Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to introduce dynamic notions into logical computational systems. The fundamental notions of proposition and truth-value in standard logic are subsumed…
Scientific computation is a discipline that combines numerical analysis, physical understanding, algorithm development, and structured programming. Several yottacycles per year on the world's largest computers are spent simulating problems…
Scientific reasoning, the process through which humans apply logic, evidence, and critical thinking to explore and interpret scientific phenomena, is essential in advancing knowledge reasoning across diverse fields. However, despite…
Neural-symbolic methods have demonstrated efficiency in enhancing the reasoning abilities of large language models (LLMs). However, existing methods mainly rely on syntactically mapping natural languages to complete formal languages like…
Large Language Models (LLMs) have demonstrated strong performance across a wide range of tasks, yet they still struggle with complex mathematical reasoning, a challenge fundamentally rooted in deep structural dependencies. To address this…
When performing complex multi-step reasoning tasks, the ability of Large Language Models (LLMs) to derive structured intermediate proof steps is important for ensuring that the models truly perform the desired reasoning and for improving…
The aim of this paper is to introduce a logic in which nouns and verbs are handled together as a deductive reasoning, and also to observe the relationship between nouns and verbs as well as between logics and conversations.
We establish a novel connection between two research areas in non-classical logics which have been developed independently of each other so far: on the one hand, input/output logic, introduced within a research program developing logical…
Explanation constitutes an archetypal feature of human rationality, underpinning learning and generalisation, and representing one of the media supporting scientific discovery and communication. Due to the importance of explanations in…
Deontic logic is a very well researched branch of mathematical logic and philosophy. Various kinds of deontic logics are discussed for different application domains like argumentation theory, legal reasoning, and acts in multi-agent…
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…
We encode arrays as functions which, in turn, are encoded as sets of ordered pairs. The set cardinality of each of these functions coincides with the length of the array it is representing. Then we define a fragment of set theory that is…
The problem of giving a computational meaning to classical reasoning lies at the heart of logic. This article surveys three famous solutions to this problem - the epsilon calculus, modified realizability and the dialectica interpretation -…
We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…
Philosophy of science attempts to describe all parts of the scientific process in a general way in order to facilitate the description, execution and improvements of this process. So far, all proposed philosophies have only covered existing…
Reasoning is a distinctive human-like characteristic attributed to LLMs in HCI due to their ability to simulate various human-level tasks. However, this work argues that the reasoning behavior of LLMs in HCI is often decontextualized from…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
Symbolic logical reasoning is a critical yet underexplored capability of large language models (LLMs), providing reliable and verifiable decision-making in high-stakes domains such as mathematical reasoning and legal judgment. In this…