Related papers: Hyperformalism for Bunched Natural Deduction Syste…

In this paper a conditional logic is defined and studied. This conditional logic, Deterministic Bayesian Logic, is constructed as a deterministic counterpart to the (probabilistic) Bayesian conditional. The logic is unrestricted, so that…

Abductive explanations (AXp's) are widely used for understanding decisions of classifiers. Existing definitions are suitable when features are independent. However, we show that ignoring constraints when they exist between features may lead…

We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on…

Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform…

Large Language Models (LLMs) have transformed natural language processing and hold growing promise for advancing science, healthcare, and decision-making. Yet their training paradigms remain dominated by affirmation-based inference, akin to…

Transformers have been shown to be able to perform deductive reasoning on a logical rulebase containing rules and statements written in English natural language. While the progress is promising, it is currently unclear if these models…

Superposition is an established decision procedure for a variety of first-order logic theories represented by sets of clauses. A satisfiable theory, saturated by superposition, implicitly defines a minimal term-generated model for the…

We consider uniform random permutations in classes having a finite combinatorial specification for the substitution decomposition. These classes include (but are not limited to) all permutation classes with a finite number of simple…

In the present paper, the existence and multiplicity problems of extensions are addressed. The focus is on extension of the stable type. The main result of the paper is an elegant characterization of the existence and multiplicity of…

We propose a new method, using deformation theory, to study the maximal rank conjecture. For line bundles of extremal degree, which can be viewed as the first case to test the conjecture, we prove that maximal rank conjecture holds by our…

The paper is devoted to modal properties of the ternary strict betweenness relation as used in the development of various systems of geometry. We show that such a relation is non-definable in a basic similarity type with a binary operator…

Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…

A paradefinite logic is a logic that can serve as the underlying logic for theories that are inconsistent or incomplete. A well-known paradefinite logic is Belnap-Dunn logic. Various expansions of Belnap-Dunn logic have been studied in the…

Induction is the process by which we obtain predictive laws or theories or models of the world. We consider the structural aspect of induction. We answer the question as to whether we can find a finite and minmalistic set of operations on…

We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…

The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…

In this paper we provide a first analysis of the research questions that arise when dealing with the problem of communicating pieces of formal argumentation through natural language interfaces. It is a generally held opinion that formal…

Abstraction is a powerful idea widely used in science, to model, reason and explain the behavior of systems in a more tractable search space, by omitting irrelevant details. While notions of abstraction have matured for deterministic…

It is shown how to extend the formal variational calculus in order to incorporate integrals of divergences into it. Such a generalization permits to study nontrivial boundary problems in field theory on the base of canonical formalism.

Bayesian networks provide an elegant formalism for representing and reasoning about uncertainty using probability theory. Theyare a probabilistic extension of propositional logic and, hence, inherit some of the limitations of propositional…