Related papers: Pragmatic Nonsense
This paper examines the application of Tarski's Undefinability Theorem to first-order arithmetic. The generally accepted view is that for this case the Theorem establishes that arithmetic truth is not arithmetic. A careful examination of…
We study the structure of the partial order induced by the definability relation on definitions of truth for the language of arithmetic. Formally, a definition of truth is any sentence $\alpha$ which extends a weak arithmetical theory…
Reasoning has long been understood as a pathway between stages of understanding. Proper reasoning leads to understanding of a given subject. This reasoning was conceptualized as a process of understanding in a particular way, i.e.,…
Language is not only used to transmit neutral information; we often seek to persuade by arguing in favor of a particular view. Persuasion raises a number of challenges for classical accounts of belief updating, as information cannot be…
It is argued that the traditional "realist" methodology of physics, according to which human concepts, laws and theories can grasp the essence of reality, is incompatible with the most fruitful interpretation of quantum formalism. The proof…
\textbf{T-BAT} logic is a formal system designed to express the notion of informal provability. This type of provability is closely related to mathematical practice and is quite often contrasted with formal provability, understood as a…
Beginning with a simple semantics for propositions, based on counting observations, it is shown that probabilistic and fuzzy logic correspond to two different heuristic assumptions regarding the combination of propositions whose evidence…
The importance of transformations and normal forms in logic programming, and generally in computer science, is well documented. This paper investigates transformations and normal forms in the context of Defeasible Logic, a simple but…
A true lie is a lie that becomes true when announced. In a logic of announcements, where the announcing agent is not modelled, a true lie is a formula (that is false and) that becomes true when announced. We investigate true lies and other…
Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…
In this paper a class of languages which are formal enough for mathematical reasoning is introduced. First-order formal languages containing natural numbers and numerals belong to that class. Its languages are called mathematically…
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…
Much has been discussed in the philosophy of science about how we should understand the scientific enterprise. On the one hand, scientific realists believe that empirically adequate theories can be supplemented by interpretations that can…
Defeasible logics provide several linguistic features to support the expression of defeasible knowledge. There is also a wide variety of such logics, expressing different intuitions about defeasible reasoning. However, the logics can only…
The fundamental proposal in this article is that logical formulas of the form (f <-> ~f) are not contradictions, and that formulas of the form (t <-> t) are not tautologies. Such formulas, wherever they appear in mathematics, are instead…
The ability to accurately interpret implied meanings plays a crucial role in human communication and language use, and language models are also expected to possess this capability. This study demonstrates that providing language models with…
Informal logic is a method of argument analysis which is complementary to that of formal logic, providing for the pragmatic treatment of features of argumentation which cannot be reduced to logical form. The central claim of this paper is…
We prove the equivalence of the semantic version of Tarski's theorem on the undefinability of truth with a semantic version of the Diagonal Lemma, and also show the equivalence of syntactic Tarski's Undefinability Theorem with a weak…
There are many ways we can not know. Even in systems that we created ourselves, as, for example, systems in mathematical logic, Go\"edel and Tarski's theorems impose limits on what we can know. As we try to speak of the real world, things…
Standard information theory says nothing about how much meaning is conveyed by a message. We fill this gap with a rigorously justifiable, quantitative definition of ``pragmatic information'', the amount of meaning in a message relevant to a…