Related papers: Classifying Material Implications over Minimal Log…

Different notions of the consistency of obligations collapse in standard deontic logic. In justification logics, which feature explicit reasons for obligations, the situation is different. Their strength depends on a constant specification…

Although logical consistency is desirable in scientific research, standard statistical hypothesis tests are typically logically inconsistent. In order to address this issue, previous work introduced agnostic hypothesis tests and proved that…

Paradoxes are a relatively frequent occurrence in physics. The nature of their genesis is diverse and they are found in all branches of physics. There are a number of general and special classifications of paradoxes, but there are no…

Intuitionistic logic, in which the double negation law not-not-P = P fails, is dominant in categorical logic, notably in topos theory. This paper follows a different direction in which double negation does hold. The algebraic notions of…

Varieties with log terminal and log canonical singularities are considered in the Minimal Model Program, see \cite{...} for introduction. In \cite{shokurov:hyp} it was conjectured that many of the interesting sets, associated with these…

While argument mining has achieved significant success in classifying argumentative relations between statements (support, attack, and neutral), we have a limited computational understanding of logical mechanisms that constitute those…

This paper investigates logical consequence defined in terms of probability distributions, for a classical propositional language using a standard notion of probability. We examine three distinct probabilistic consequence notions, which we…

While explainability is a desirable characteristic of increasingly complex black-box models, modern explanation methods have been shown to be inconsistent and contradictory. The semantics of explanations is not always fully understood - to…

Over the past few years, the abilities of large language models (LLMs) have received extensive attention, which have performed exceptionally well in complicated scenarios such as logical reasoning and symbolic inference. A significant…

This paper presents a study of how the theory of categories leads to the creation of non classical logical systems. In particular, the case of the elementary topos of graphs, where there are three other truth values different from false and…

This paper undertakes a foundational inquiry into logical inferentialism with particular emphasis on the normative standards it establishes and the implications these pose for classical logic. The central question addressed herein is: 'What…

The paradoxes of the double-slit and the EPR experiments with particles are shown to originate in the implicit assumption that the particles are always located in the classical space. It is demonstrated that there exists a natural…

We combine linear temporal logic (with both past and future modalities) with a deontic version of justification logic to provide a framework for reasoning about time and epistemic and normative reasons. In addition to temporal modalities,…

Extensional higher-order logic programming has been introduced as a generalization of classical logic programming. An important characteristic of this paradigm is that it preserves all the well-known properties of traditional logic…

The \it{Ambient Logic} (AL) has been proposed for expressing properties of process mobility in the calculus of Mobile Ambients (MA), and as a basis for query languages on semistructured data. We study some basic questions concerning the…

This work is divided between two main areas: in the theory of multialgebras, we focus mostly on a new definition of what a freely generated object should be in their category, and on how this category is equivalent to another with partially…

Debates concerning philosophical grounds for the validity of classical and intuitionistic logics often have the very nature of logical proofs as one of the main points of controversy. The intuitionist advocates for a strict notion of…

Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit…

Inclusion logic is a variant of dependence logic that was shown to have the same expressive power as positive greatest fixed-point logic. Inclusion logic is not axiomatizable in full, but its first-order consequences can be axiomatized. In…

A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the…