Related papers: Teaching Logics through Their Philosophical Commit…
This 2024 chapter gives a brief overview of cognitive and educational sciences' perspectives on learning outcomes (LOs) to facilitate the integration of LOs specific to ethical reasoning into any mathematics or quantitative course. The…
Lewis' theory of counterfactuals is the foundation of many contemporary notions of causality. In this paper, we extend this theory in the temporal direction to enable symbolic counterfactual reasoning on infinite sequences, such as…
Classes of linguistic paradoxes and linguistic tautologies are introduced with examples and explanations. They are part of the author's work on the Paradoxist Philosophy based on mathematical logic. The general cases exposed below are…
Theory based AI research has had a hard time recently and the aim here is to propose a model of what LLMs are actually doing when they impress us with their language skills. The model integrates three established theories of human…
Drawing on the Data and Predictions strand of the Indicazioni Nazionali per il curricolo 2012, this study proposes a problem based instructional approach to the teaching of probability. More specifically, the study adopts a design based…
We describe a general approach to deriving linear-time logics for a wide variety of state-based, quantitative systems, by modelling the latter as coalgebras whose type incorporates both branching and linear behaviour. Concretely, we define…
We present a way to apply quantum logic to the study of quantum programs. This is made possible by using an extension of the usual propositional language in order to make transformations performed on the system appear explicitly. This way,…
We discuss the problem of defining a logic for analogical reasoning, and sketch a solution in the style of the semantics for Counterfactual Conditionals, Preferential Structures, etc.
This paper tries to justify the relevance of an introductory course in Mathematical Logic in the Philosophy curriculum for analyzing philosophical arguments in natural language. It is argued that the representation of the structure of…
We seize the opportunity of the publication of selected papers from the \emph{Logic, categories, semantics} workshop in the \emph{Journal of Applied Logic} to survey some current trends in logic, namely intuitionistic and linear type…
The ability to conduct logical reasoning is a fundamental aspect of intelligent human behavior, and thus an important problem along the way to human-level artificial intelligence. Traditionally, logic-based symbolic methods from the field…
We introduce the relational ontology log, or relational olog, a knowledge representation system based on the category of sets and relations. It is inspired by Spivak and Kent's olog, a recent categorical framework for knowledge…
We believe, in the sense of supporting ideas and considering them correct while dismissing doubts about them. We take sides about ideas and theories as if that was the right thing to do. And yet, from a rational point of view, this type of…
On the one hand, classical logic is an extremely successful theory, even if not being perfect. On the other hand, intuitionistic logic is, without a doubt, one of the most important non-classical logics. But, how can proponents of one logic…
We argue that logical semantics might have faltered due to its failure in distinguishing between two fundamentally very different types of concepts: ontological concepts, that should be types in a strongly-typed ontology, and logical…
The formal construction of the second-order logic or predicate calculus essentially adds quantifiers to propositional logic. Why second-order logic cannot be reduced to that of the first order? How to demonstrate that certain predicates are…
Applying logic in the area of conceptual modeling has been investigated widely, yet there has been limited uptake of logic-based conceptual modeling in industry. According to some researchers, another formalization of such tools as EER or…
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…
In the present article the necessity of introducing the teaching of time from the first educative stages is defended through a didactic process in which a feedback is produced between its chronological dimension (perception and measuring of…
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…