Related papers: How to Make a New Logic

Texts present coherent stories that have a particular theme or overall setting, for example science fiction or western. In this paper, we present a text generation method called {\it rewriting} that edits existing human-authored narratives…

Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…

We introduce and study single-conclusioned nested sequent calculi for a broad class of intuitionistic multi-modal logics known as "intuitionistic grammar logics (IGLs)." These logics serve as the intuitionistic counterparts of classical…

We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…

We consider modeling the conception of knowledge in terms of temporal logic. The study of knowledge logical operations is originated around 1962 by representation of knowledge and belief using modalities. Nowadays, it is very good…

This paper studies learning logic rules for reasoning on knowledge graphs. Logic rules provide interpretable explanations when used for prediction as well as being able to generalize to other tasks, and hence are critical to learn. Existing…

I have developed a pedagogy and textbook for teaching logic centered on what I call "logical worldviews". A logical worldview examines the close connection between philosophical commitments and the logical principles and method for a…

One main goal of argumentation theory is to evaluate arguments and to determine whether they should be accepted or rejected. When there is no clear answer, a third option, being undecided, has to be taken into account. Indecision is often…

Logic is a foundation for many modern areas of computer science. In artificial intelligence, as a basis of database query languages, as well as in formal software and hardware verification --- modelling scenarios using logical formalisms…

Temporal logic rules are often used in control and robotics to provide structured, human-interpretable descriptions of trajectory data. These rules have numerous applications including safety validation using formal methods, constraining…

Artificial intelligence systems exhibit many useful capabilities, but they appear to lack understanding. This essay describes how we could go about constructing a machine capable of understanding. As John Locke (1689) pointed out words are…

The purpose of this paper is to introduce justification logics based on conditional logics. We introduce a new family of logics, called conditional justification logics, which incorporates a counterfactual conditional in its language. For…

When humans solve complex problems, they typically create a sequence of ideas (involving an intuitive decision, reflection, error correction, etc.) in order to reach a conclusive decision. Contrary to this, today's models are mostly trained…

Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…

This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…

Humans invent new words when there is a rising demand for a new useful concept (e.g., doomscrolling). We explore and validate a similar idea in our communication with LLMs: introducing new words to better understand and control the models,…

The concept of a judgment as a logical action which introduces new information into a deductive system is examined. This leads to a way of mathematically representing implication which is distinct from the familiar material implication,…

Epistemic logic is known as a logic that captures the knowledge and beliefs of agents and has undergone various developments since Hintikka (1962). In this paper, we propose a new logic called agent-knowledge logic by taking the product of…

First-Order Logic (FOL) is widely regarded as one of the most important foundations for knowledge representation. Nevertheless, in this paper, we argue that FOL has several critical issues for this purpose. Instead, we propose an…

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…