Related papers: Logic in Mathematics and Computer Science
Mastering one or more programming languages has historically been the gateway to implementing ideas on a computer. Today, that gateway is widening with advances in large language models (LLMs) and artificial intelligence (AI)-powered coding…
Mathematics cannot anymore be assimilated to a linguistic game, where formal proofs are strongly differentiated with conjectural thinking, without building any category of knowledge to understand the passage (Wittgenstein's gist). Nowadays,…
Cybersecurity demands rigorous and scalable techniques to ensure system correctness, robustness, and resilience against evolving threats. Automated reasoning, encompassing formal logic, theorem proving, model checking, and symbolic…
Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to reveal the dynamical notions inherent in logical computational systems. The fundamental notions of proposition and truth-value in standard logic…
The ForMaRE project applies formal mathematical reasoning to economics. We seek to increase confidence in economics' theoretical results, to aid in discovering new results, and to foster interest in formal methods, i.e. computer-aided…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
The basic notions of logic-predicate logic, Peano arithmetic, incompleteness theorems, etc.-have for long been an advanced topic. In the last decades, they became more widely taught, inphilosophy, mathematics, and computer science…
Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been…
Logic programming languages present clear advantages in terms of declarativeness and conciseness. However, the ideas of logic programming have been met with resistance in other programming communities, and have not generally been adopted by…
Since its existence, the computer tool has often supported mathematicians, whether it is to implement an approximation method (numerical calculation of a root, of an integral, ...) or to simulate a phenomenon (geometric in nature,…
Traditional treatments of formal logic provide: 1. A syntax for formulas. 2. An inference relation between sets of formulas. 3. A rule for assigning meaning to formulas (semantics) that is sound with respect to the inference relation. First…
In the last decades, several objects such as grammars, economical agents, laws of physics... have been defined as algorithms. In particular, after Brouwer, Heyting, and Kolomogorov, mathematical proofs have been defined as algorithms. In…
A simple framework for reasoning under uncertainty and intervention is introduced. This is achieved in three steps. First, logic is restated in set-theoretic terms to obtain a framework for reasoning under certainty. Second, this framework…
An origin is often an intriguing issue. It becomes doubly intriguing when the logical form of thinking is considered. In this paper we will investigate exactly that: we will conjecture on the origin of basic instruments of logical thinking.…
Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to…
This work examines the interconnections between logic, epistemology, and sciences within the Naturalist tradition. It presents a scheme that connects logic, mathematics, physics, chemistry, biology, and cognition, emphasizing…
Although quantum states nicely explain experiments, the outcomes of experiments are not states. Instead, outcomes correspond to probability distributions. Twenty years ago we proved categorically that probability distributions leave open a…
We present algebraic semantics for the classical logic of proofs based on Boolean algebras. We also extend the language of the logic of proofs in order to have a Boolean structure on justification terms and equality predicate on terms. In…
The past few years have seen a surge of interest in the field of probabilistic logic learning and statistical relational learning. In this endeavor, many probabilistic logics have been developed. ProbLog is a recent probabilistic extension…
Using an algebraic framework we solve a problem posed in [5] and [7] about the axiomatizability of a quantum computational type logic related to fuzzy logic. A Hilbert-style calculus is developed obtaining an algebraic strong completeness…