Related papers: A proof-theoretic approach to abstract interpretat…
The framework of quantitative equational logic has been successfully applied to reason about algebras whose carriers are metric spaces and operations are nonexpansive. We extend this framework in two orthogonal directions: algebras endowed…
It is known that any rational abstract numeration system is faithfully, and effectively, represented by an N-rational series. A simple proof of this result is given which yields a representation of this series which in turn allows a simple…
We introduce a novel variant of logical relations that maps types not merely to partial equivalence relations on values, as is commonly done, but rather to a proof-relevant generalisation thereof, namely setoids. The objects of a setoid…
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…
We try to bring to light some combinatorial structure underlying formal proofs in logic. We do this through the study of the Craig Interpolation Theorem which is properly a statement about the structure of formal derivations. We show that…
Formal concept analysis has grown from a new branch of the mathematical field of lattice theory to a widely recognized tool in Computer Science and elsewhere. In order to fully benefit from this theory, we believe that it can be enriched…
Textual logical reasoning, especially question-answering (QA) tasks with logical reasoning, requires awareness of particular logical structures. The passage-level logical relations represent entailment or contradiction between propositional…
In recent years, large language models (LLMs) have made significant advancements in developing human-like and engaging dialogue systems. However, in tasks such as consensus-building and persuasion, LLMs often struggle to resolve conflicts…
As the second part of the treatise 'A General Theory of Concept Lattice', this paper speaks of the tractability of the general concept lattice for both its lattice structure and logic content. The general concept lattice permits a feasible…
We extend \L ukasiewicz logic obtaining the infinitary logic $\mathcal{IR}\L$ whose models are algebras $C(X,[0,1])$, where $X$ is a basically disconnected compact Hausdorff space. Equivalently, our models are unit intervals in…
Proofs are traditionally syntactic, inductively generated objects. This paper reformulates first-order logic (predicate calculus) with proofs which are graph-theoretic rather than syntactic. It defines a combinatorial proof of a formula…
Quantum computational logics represent a logical abstraction from the circuit-theory in quantum computation. In these logics formulas are supposed to denote pieces of quantum information (qubits, quregisters or mixtures of quregisters),…
We study abstract intermediate justification logics, that is arbitrary intermediate propositional logics extended with a subset of specific axioms of (classical) justification logics. For these, we introduce various semantics by combining…
Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of set-valued mappings between function spaces. This paper deals with the computational properties of certain…
We introduce and study logic programs whose clauses are built out of monotone constraint atoms. We show that the operational concept of the one-step provability operator generalizes to programs with monotone constraint atoms, but the…
We consider abstraction-based design of output-feedback controllers for non-linear dynamical systems against specifications over state-based predicates in linear-time temporal logic (LTL). In this context, our contribution is two-fold: (I)…
I explore the relationships between Prawitz's approach to non-monotonic proof-theoretic validity, which I call reducibility semantics, and some later proof-theoretic approaches, which I call standard base semantics and Sandqvist's base…
Neural networks excel at pattern recognition but struggle with reliable logical reasoning, often violating basic logical principles during inference. We address this limitation by developing a categorical framework that systematically…
This paper describes a procedure that system developers can follow to translate typical mathematical representations of linearized control systems into logic theories. These theories are then used to verify system requirements and find…
The intention of the present study is to establish the mathematical fundamentals for automated problem solving essentially targeted for robotics by approaching the task universal algebraically introducing knowledge as realizations of…