Related papers: On the Various Translations between Classical, Int…
Physics is formulated in terms of timeless classical mathematics. A formulation on the basis of intuitionist mathematics, built on time-evolving processes, would offer a perspective that is closer to our experience of physical reality.
We show that intuitionistic propositional logic is \emph{Carnap categorical}: the only interpretation of the connectives consistent with the intuitionistic consequence relation is the standard interpretation. This holds relative to the most…
We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present…
Traditional neural networks have an impressive classification performance, but what they learn cannot be inspected, verified or extracted. Neural Logic Networks on the other hand have an interpretable structure that enables them to learn a…
In this paper we make a contribution to the unification of formal models of defeasible reasoning. We present several translations between formal argumentation frameworks and nonmonotonic logics for reasoning with plausible assumptions. More…
We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path…
The importance of intuitionistic temporal logics in Computer Science and Artificial Intelligence has become increasingly clear in the last few years. From the proof-theory point of view, intuitionistic temporal logics have made it possible…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
Lexical semantics theories differ in advocating that the meaning of words is represented as an inference graph, a feature mapping or a vector space, thus raising the question: is it the case that one of these approaches is superior to the…
We investigate four well-known negative translations of classical logic into intuitionistic logic within a substructural setting. We find that in affine logic the translation schemes due to Kolmogorov and G\"odel both satisfy Troelstra's…
Several authors have recently defined intuitionistic logic based on team semantics (tIPC). In this paper we provide two alternative approaches to intermediate logics in the team semantics setting. We do this by modifying tIPC with axioms…
It is well-known that the size of propositional classical proofs can be huge. Proof theoretical studies discovered exponential gaps between normal or cut free proofs and their respective non-normal proofs. The aim of this work is to study…
We introduce the calculus of Classical Transitions (CT), which extends the research line on the relationship between linear logic and processes to labelled transitions. The key twist from previous work is registering parallelism in typing…
Abstraction logic is a new logic, serving as a foundation of mathematics. It combines features of both predicate logic and higher-order logic: abstraction logic can be viewed both as higher-order logic minus static types as well as…
A large amount of research about multimodal inference across text and vision has been recently developed to obtain visually grounded word and sentence representations. In this paper, we use logic-based representations as unified meaning…
While the traditional conception of inductive logic is Carnapian, I develop a Peircean alternative and use it to unify formal learning theory, statistics, and a significant part of machine learning: supervised learning. Some crucial…
One way of proving theorems in modal logics is translating them into the predicate calculus and then using conventional resolution-style theorem provers. This approach has been regarded as inappropriate in practice, because the resulting…
The difference between object-language and metalanguage is crucial for logical analysis, but has yet not been examined for the field of computer science. In this paper the difference is examined with regard to inferential relations. It is…
Two lines of approaches are adopted for complex reasoning with LLMs. One line of work prompts LLMs with various reasoning structures, while the structural outputs can be naturally regarded as intermediate reasoning steps. Another line of…
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…