Related papers: Negational Fragment of Intuitionistic Control Logi…

Prompt-based methods have gained increasing attention on NLP and shown validity on many downstream tasks. Many works have focused on mining these methods' potential for knowledge extraction, but few explore their ability to make logical…

We look at non-classical negations and their corresponding adjustment connectives from a modal viewpoint, over complete distributive lattices, and apply a very general mechanism in order to offer adequate analytic proof systems to logics…

In-Context Learning (ICL) has emerged as an important new paradigm in natural language processing and large language model (LLM) applications. However, the theoretical understanding of the ICL mechanism remains limited. This paper aims to…

Despite great performance on many tasks, language models (LMs) still struggle with reasoning, sometimes providing responses that cannot possibly be true because they stem from logical incoherence. We call such responses \textit{strong…

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…

This paper treats logic programming with three kinds of negation: default, weak and strict negations. A 3-valued logic model theory is discussed for logic programs with three kinds of negation. The procedure is constructed for negations so…

Logical bilateralism challenges traditional concepts of logic by treating assertion and denial as independent yet opposed acts. While initially devised to justify classical logic, its constructive variants show that both acts admit…

On the one hand, classical logic is an extremely successful theory, even if not being perfect. On the other hand, intuitionistic logic is, without a doubt, one of the most important non-classical logics. But, how can proponents of one logic…

With the increasing empirical success of distributional models of compositional semantics, it is timely to consider the types of textual logic that such models are capable of capturing. In this paper, we address shortcomings in the ability…

In [1], systems of weakening of intuitionistic negation logic called Z_n and CZ_n were developed in the spirit of da Costa's approach(c.f. [2]) by preserving, differently from da Costa, its fundamental properties: antitonicity, inversion…

Motivated by applications to string processing, we introduce variants of the Lyndon factorization called inverse Lyndon factorizations. Their factors, named inverse Lyndon words, are in a class that strictly contains anti-Lyndon words, that…

We say that a logic L has the Lyndon positivity property (LPP) if all formulas which are monotone in L (that is, are preserved under increasing the valuation on L-algebras) are L-equivalent to positive formulas (formulas without negation…

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)}…

In-context learning (ICL) is a new paradigm for natural language processing (NLP), where a large language model (LLM) observes a small number of demonstrations and a test instance as its input, and directly makes predictions without…

Intuitionistic grammar logics fuse constructive and multi-modal reasoning while permitting the use of converse modalities, serving as a generalization of standard intuitionistic modal logics. In this paper, we provide definitions of these…

In this article we show how Hans Kelsen jurisprudence and Intuitionistic logic are used to avoid the well-known contrary-to-duty (CTD) paradoxes, such as Chisholm paradoxes and its variants. This article uses an intuitionistic version of…

Possibilistic logic is a well-known graded logic of uncertainty suitable to reason under incomplete information and partially inconsistent knowledge, which is built upon classical first order logic. There exists for Possibilistic logic a…

This paper develops a novel nested sequent proof-search methodology for intuitionistic tense logics (ITLs), supporting finite counter-model extraction. We introduce a new loop-checking method that detects repeating nested sequents using…

Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator capturing the most typical (alias normal or conventional) situations in which a given sentence…

Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html ) is a research program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which it has more traditionally been.…