Related papers: Logic: A Misleading Concept. A Contradiction Study…

In the past century many fundamental results on unpredictability, undecidability and uncertainty have compelled scientists to grapple with the idea that some questions may never be resolved within our current theories. While this…

Computability logic is a formal theory of (interactive) computability in the same sense as classical logic is a formal theory of truth. This approach was initiated very recently in "Introduction to computability logic" (Annals of Pure and…

There has been a recent resurgence in the area of explainable artificial intelligence as researchers and practitioners seek to make their algorithms more understandable. Much of this research is focused on explicitly explaining decisions or…

The introduction of explicit notions of rejection, or disbelief, into logics for knowledge representation can be justified in a number of ways. Motivations range from the need for versions of negation weaker than classical negation, to the…

We introduce a new semantics for justification logic based on subset relations. Instead of using the established and more symbolic interpretation of justifications, we model justifications as sets of possible worlds. We introduce a new…

An inductive logic can be formulated in which the elements are not propositions or probability distributions, but information systems. The logic is complete for information systems with binary hypotheses, i.e., it applies to all such…

The work reported here introduces Defeasible Logic Programming (DeLP), a formalism that combines results of Logic Programming and Defeasible Argumentation. DeLP provides the possibility of representing information in the form of weak rules…

Proofs, in Ludics, have an interpretation provided by their counter-proofs, that is the objects they interact with. We follow the same idea by proposing that sentence meanings are given by the counter-meanings they are opposed to in a…

Neutrosophic Over-/Under-/Off-Set and -Logic were defined by the author in 1995 and published for the first time in 2007. We extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is over 1},…

In their position paper entitled "Towards a new, complexity science of learning and education", Jorg et al. (2007) argue that educational research is in crisis. In their opinion, the transdisciplinary and interdiscursive approach of…

In this article we present and describe a notion of "logical perfection". We extract the notion of "perfection" from the contemporary logical concept of categoricity. Categoricity (in power) has become in the past half century a main driver…

Although the so called tetralemma might seem to be incompatible with any recognized scheme of logical inference, its four alternatives arise naturally within the anhomomorphic logics which have been proposed in order to accommodate certain…

Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…

This paper aims to justify the concept of natural intelligence, the type of intelligence wider than human intelligence and its derivative, AI. I will argue that the process of life is a cognitive process and that organisms, from bacteria to…

The class of defeasible logics is only vaguely defined -- it is defined by a few exemplars and the general idea of efficient reasoning with defeasible rules. The recent definition of the defeasible logic $DL(\partial_{||})$ introduced new…

Rule-based explanation methods offer rigorous and globally interpretable insights into neural network behavior. However, existing approaches are mostly limited to small fully connected networks and depend on costly layerwise rule extraction…

Research in AI using Large-Language Models (LLMs) is rapidly evolving, and the comparison of their performance with human reasoning has become a key concern. Prior studies have indicated that LLMs and humans share similar biases, such as…

In this paper, we present a preliminary work on an approach to fill the gap between logic-based argumentation and the numerous approaches to tackle the dynamics of abstract argumentation frameworks. Our idea is that, even when arguments and…

We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a…

Logical reasoning is essential in a variety of human activities. A representative example of a logical task is mathematics. Recent large-scale models trained on large datasets have been successful in various fields, but their reasoning…