Related papers: Intuitionistic Logic is a Connexive Logic
Intuitive learning is crucial for developing deep conceptual understanding, especially in STEM education, where students often struggle with abstract and interconnected concepts. Automatic question generation has become an effective…
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…
Inconsistencies are ubiquitous in law, administration, and jurisprudence. Though a cure is too much to hope for, we propose a technological remedy. Large language models (LLMs) can accurately extract propositions from arguments and compile…
We extend description logics (DLs) with non-monotonic reasoning features. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann and Magidor in the propositional…
We give an algebraic proof of the criterion for hereditary structural completeness of an intermediate logic, or, equivalently, of the primitiveness of a variety of Heyting algebras.
Inspired by the curvature of space-time (Einstein, 1921), we introduce Curved Contrastive Learning (CCL), a novel representation learning technique for learning the relative turn distance between utterance pairs in multi-turn dialogues. The…
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 study the system IFP of intuitionistic fixed point logic, an extension of intuitionistic first-order logic by strictly positive inductive and coinductive definitions. We define a realizability interpretation of IFP and use it to extract…
Session type systems have been given logical foundations via Curry-Howard correspondences based on both intuitionistic and classical linear logic. The type systems derived from the two logics enforce communication correctness on the same…
Gentzen-style sequent calculi and Gentzen-style natural deduction systems are introduced for a family (C-family) of connexive logics over Wansing's basic connexive logic C. The C-family is derived from C by incorporating the Peirce law, the…
The need for rigorous process composition is encountered in many situations pertaining to the development and analysis of complex systems. We discuss the use of Classical Linear Logic (CLL) for correct-by-construction resource-based process…
Pre-trained language models (PLMs) have made significant advances in natural language inference (NLI) tasks, however their sensitivity to textual perturbations and dependence on large datasets indicate an over-reliance on shallow…
We revisit the notion of intuitionistic equivalence and formal proof representations by adopting the view of formulas as exponential polynomials. After observing that most of the invertible proof rules of intuitionistic (minimal)…
In this book we promote logical computational linguistics as opposed to statistical computational linguistics. In particular, we provide a logical semantic interface. This book assembles more than twenty years of research work on type…
We introduce the concept of access-based intuitionistic knowledge which relies on the intuition that agent $i$ knows $\varphi$ if $i$ has found access to a proof of $\varphi$. Basic principles are distribution and factivity of knowledge as…
We introduce and develop a topological semantics of conservativity logics and interpretability logics. We prove the topological compactness theorem of consistent normal extensions of the conservativity logic $\mathbf{CL}$ by extending…
Large language models (LLMs) often struggle with complex mathematical tasks, prone to "hallucinating" incorrect answers due to their reliance on statistical patterns. This limitation is further amplified in average Small LangSLMs with…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
Scott's information systems provide a categorically equivalent, intensional description of Scott domains and continuous functions. Following a well established pattern in denotational semantics, we define a linear version of information…
The article explores the arithmetic of multiplication as a model of many valued projective logic. It is demonstrated that closed numerical intervals within this framework constitute Heyting algebras. The conditions for these algebras to be…