相关论文: Formal semantics of language and the Richard-Berry…
Intuitively, the more powerful a theory is, the greater the variety and quantity of ideas can be expressed through its formal language. Therefore, when comparing two theories concerning the same subject, it seems only reasonable to compare…
In the paper, using the language of spin-half particles, Hardy's paradox is examined within different semantics: a partial one, a many-valued one, and one defined as a set of weak values of projection operators. As it is shown in this…
We analyze the informal notion of truth and conclude that it can be formalized in essentially two distinct ways: constructively, in terms of provability, or classically, as a hierarchy of concepts which satisfy Tarski's biconditional in…
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…
As transformers have gained prominence in natural language processing, some researchers have investigated theoretically what problems they can and cannot solve, by treating problems as formal languages. Exploring such questions can help…
Formal languages are essential for computer programming and are constructed to be easily processed by computers. In contrast, natural languages are much more challenging and instigated the field of Natural Language Processing (NLP). One…
This paper investigates how global decision problems over arithmetically represented domains acquire reflective structure through class-quantification. Arithmetization forces diagonal fixed points whose verification requires reflection…
The semantic paradoxes are associated with self-reference or referential circularity. However, there are infinitary versions of the paradoxes, such as Yablo's paradox, that do not involve this form of circularity. It remains an open…
Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…
A classic account of the quantification of semantic information is that of Bar-Hiller and Carnap. Their account proposes an inverse relation between the informativeness of a statement and its probability. However, their approach assigns the…
Proofs, in Ludics, have an interpretation provided by their counter-proofs, that is the objects they interact with. We follow the same idea by proposing that sentence meanings are given by the counter-meanings they are opposed to in a…
Modern Logics, as formulated notably by Frege, Russell and Tarski involved basic assumptions about Natural Languages in general and Indo-European Languages in particular, which are contested by Linguists. Based upon those assumptions,…
Recent papers in explainable AI have made a compelling case for counterfactual modes of explanation. While counterfactual explanations appear to be extremely effective in some instances, they are formally equivalent to adversarial examples.…
Paradoxes are interesting puzzles in philosophy and mathematics, and they could be even more fascinating, when turned into proofs and theorems. For example, Liar's paradox can be translated into a propositional tautology, and Barber's…
This paper presents a formal theory which describes propositional binary logic as a semantically closed formal language, and allows for syntactically and semantically well-formed formulae, formal proofs (demonstrability in Hilbertian…
The integration of lexical semantics and pragmatics in the analysis of the meaning of natural lan- guage has prompted changes to the global framework derived from Montague. In those works, the original lexicon, in which words were assigned…
The concept of informal mathematical proof considered in intuitionism is apparently vulnerable to a version of the liar paradox. However, a careful reevaluation of this concept reveals a subtle error whose correction blocks the…
The logic--linguistic structure of quantum physics is analysed. The role of formal systems and interpretations in the representation of nature is investigated. The problems of decidability, completeness, and consistency can affect quantum…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
In this article, we present a fresh perspective on language, combining ideas from various sources, but mixed in a new synthesis. As in the minimalist program, the question is whether we can formulate an elegant formalism, a universal…