Related papers: Semantic Foundations of Reductive Reasoning
Abstraction is a powerful idea widely used in science, to model, reason and explain the behavior of systems in a more tractable search space, by omitting irrelevant details. While notions of abstraction have matured for deterministic…
When reasoning in description, modal or temporal logics it is often useful to consider axioms representing universal truths in the domain of discourse. Reasoning with respect to an arbitrary set of axioms is hard, even for relatively…
Conditionals are useful for modelling, but are not always sufficiently expressive for capturing information accurately. In this paper we make the case for a form of conditional that is situation-based. These conditionals are more expressive…
A logic is defined that allows to express information about statistical probabilities and about degrees of belief in specific propositions. By interpreting the two types of probabilities in one common probability space, the semantics given…
This paper gives a generative model of the interpretation of formal logic for data-driven logical reasoning. The key idea is to represent the interpretation as likelihood of a formula being true given a model of formal logic. Using the…
\textbf{T-BAT} logic is a formal system designed to express the notion of informal provability. This type of provability is closely related to mathematical practice and is quite often contrasted with formal provability, understood as a…
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…
We consider multi-agent argumentation, where each agent's view of the arguments is encoded as an argumentation framework (AF). Then we study deliberative processes than can occur on this basis. We think of a deliberative process as taking…
This paper proposes new derivations of three well-known sorting algorithms, in their functional formulation. The approach we use is based on three main ingredients: first, the algorithms are derived from a simpler algorithm, i.e. the…
The syntactic nature of logic and computation separates them from other fields of mathematics. Nevertheless, syntax has been the only way to adequately capture the dynamics of proofs and programs such as cut-elimination, and the finiteness…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
Recent advances in large language models (LLMs) have made reasoning a central benchmark for evaluating intelligence. While prior surveys focus on efficiency by examining how to shorten reasoning chains or reduce computation, this view…
In this article, we present a leap-forward expansion to the study of explainability in neural networks by considering explanations as answers to abstract reasoning-based questions. With $P$ as the prediction from a neural network, these…
In the logic programming paradigm, a program is defined by a set of methods, each of which can be executed when specific conditions are met during the current state of an execution. The semantics of these programs can be elegantly…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…
Linear logic was conceived in 1987 by Girard and, in contrast to classical logic, restricts the usage of the structural inference rules of weakening and contraction. With this, atoms of the logic are no longer interpreted as truth, but as…
Large language models have recently shown promising progress in mathematical reasoning when fine-tuned with human-generated sequences walking through a sequence of solution steps. However, the solution sequences are not formally structured…
Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of…
Deduction, induction, and abduction are fundamental reasoning paradigms, core for human logical thinking. Although improving Large Language Model (LLM) reasoning has attracted significant research efforts, the extent to which the…