Related papers: Bijective Faithful Translations among Default Logi…

We establish a natural translation from word rewriting systems to strictly positive polymodal logics. Thereby, the latter can be considered as a generalization of the former. As a corollary we obtain examples of undecidable strictly…

We study the notion of conservative translation between logics introduced by Feitosa and D'Ottaviano. We show that classical propositional logic (CPC) is universal in the sense that every finitary consequence relation over a countable set…

Multiplicative linear logic is a very well studied formal system, and most such studies are concerned with the one-sided sequent calculus. In this paper we look in detail at existing translations between a deep inference system and the…

There is knowledge. There is belief. And there is tacit agreement.' 'We may talk about objects. We may talk about attributes of the objects. Or we may talk both about objects and their attributes.' This work inspects tacit agreements on…

Large Language Models (LLMs) excel in translation among other things, demonstrating competitive performance for many language pairs in zero- and few-shot settings. But unlike dedicated neural machine translation models, LLMs are not trained…

Large language models (LLMs) are capable of generating plausible explanations of how they arrived at an answer to a question. However, these explanations can misrepresent the model's "reasoning" process, i.e., they can be unfaithful. This,…

While belief functions may be seen formally as a generalization of probabilistic distributions, the question of the interactions between belief functions and probability is still an issue in practice. This question is difficult, since the…

The multiple extension problem arises frequently in diagnostic and default inference. That is, we can often use any of a number of sets of defaults or possible hypotheses to explain observations or make Predictions. In default inference,…

Based on the notion of time translation, we develop a formalism to deal with the logic of quantum properties at different times. In our formalism it is possible to enlarge the usual notion of context to include composed properties involving…

A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…

We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…

Many formalisms combining ontology languages with uncertainty, usually in the form of probabilities, have been studied over the years. Most of these formalisms, however, assume that the probabilistic structure of the knowledge remains…

Large language models (LLMs) are a promising venue for natural language understanding and generation tasks. However, current LLMs are far from reliable: they are prone to generate non-factual information and, more crucially, to contradict…

Double-negation translations are used to encode and decode classical proofs in intuitionistic logic. We show that, in the cut-free fragment, we can simplify the translations and introduce fewer negations. To achieve this, we consider the…

Default logic encounters some conceptual difficulties in representing common sense reasoning tasks. We argue that we should not try to formulate modular default rules that are presumed to work in all or most circumstances. We need to take…

Choice revision is a sort of non-prioritized multiple revision, in which the agent partially accepts the new information represented by a set of sentences. We investigate the construction of choice revision based on a new approach to belief…

Large Language Models (LLMs) are deployed as powerful tools for several natural language processing (NLP) applications. Recent works show that modern LLMs can generate self-explanations (SEs), which elicit their intermediate reasoning steps…

Classes of linguistic paradoxes and linguistic tautologies are introduced with examples and explanations. They are part of the author's work on the Paradoxist Philosophy based on mathematical logic. The general cases exposed below are…

Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…

Relation-changing modal logics are extensions of the basic modal logic that allow changes to the accessibility relation of a model during the evaluation of a formula. In particular, they are equipped with dynamic modalities that are able to…