Related papers: Truth and meaningfulness
This paper describes an axiomatic theory BT for constructive mathematics. BT has a predicative comprehension axiom for a countable number of set types and usual combinatorial operations. BT has intuitionistic logic, is consistent with…
In Outline of a Theory of Truth, Kripke introduces some of the central concepts of the logical study of truth and paradox. He informally defines some of these -- such as groundedness and paradoxicality -- using modal locutions. We introduce…
Constructor theory seeks to express all fundamental scientific theories in terms of a dichotomy between possible and impossible physical transformations - those that can be caused to happen and those that cannot. This is a departure from…
Let $\mathcal{T}$ be any of the three canonical truth theories $\textsf{CT}^-$ (Compositional truth without extra induction), $\textsf{FS}^-$ (Friedman--Sheard truth without extra induction), and $\textsf{KF}^-$ (Kripke--Feferman truth…
Research in information systems includes a wide range of approaches which make a contribution in terms of knowledge, understanding, or practical developments. The measure of any research is, ultimately, its validity: are its finding true,…
This paper will develop a single framework for unifying, simplifying and extending our prior results about axiom systems that retain a partial knowledge of their own consistency, via an axiomatic declaration of self-consistency. Its perhaps…
We give an analysis and generalizations of some long-established constructive completeness results in terms of categorical logic and pre-sheaf and sheaf semantics. The purpose is in no small part conceptual and organizational: from a few…
The foundations of quantum mechanics have been plagued by controversy throughout the 85 year history of the field. It is argued that lack of clarity in the formulation of basic philosophical questions leads to unnecessary obscurity and…
Lewis' theory of counterfactuals is the foundation of many contemporary notions of causality. In this paper, we extend this theory in the temporal direction to enable symbolic counterfactual reasoning on infinite sequences, such as…
Functional Distributional Semantics provides a computationally tractable framework for learning truth-conditional semantics from a corpus. Previous work in this framework has provided a probabilistic version of first-order logic, recasting…
We introduce a notion of the ``explanation" of one (generalized) probabilistic model by another as particular kind of span in the category $\Prob$ of probabilistic models and morphisms. We show that explanations compose under a standard…
Scholars have wondered for a long time whether the language of quantum mechanics introduces a quantum notion of truth which is formalized by quantum logic (QL) and is incompatible with the classical (Tarskian) notion. We show that QL can be…
For any first order theory T we construct a Boolean valued model M, in which precisely the T--provable formulas hold, and in which every (Boolean valued) subset which is invariant under all automorphisms of M is definable by a first order…
I discuss the design of the method of entropic inference as a general framework for reasoning under conditions of uncertainty. The main contribution of this discussion is to emphasize the pragmatic elements in the derivation. More…
This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the…
G\"odel's second incompleteness theorem is standardly understood as showing that no sufficiently strong, consistent theory of arithmetic can prove its own consistency, a result typically interpreted against a model-theoretic background in…
The paper defends the thesis that analysis of truth problem in the context of interpretations of quantum logic allows to reveal the prospect of elicitation of specifics of the relations between quantum mechanics and quantum logic in a…
We prove that the satisfaction relation $\mathcal{N}\models\varphi[\vec a]$ of first-order logic is not absolute between models of set theory having the structure $\mathcal{N}$ and the formulas $\varphi$ all in common. Two models of set…
With recent advances in natural language processing, rationalization becomes an essential self-explaining diagram to disentangle the black box by selecting a subset of input texts to account for the major variation in prediction. Yet,…
The paper demonstrates that falsifiability is fundamental to learning. We prove the following theorem for statistical learning and sequential prediction: If a theory is falsifiable then it is learnable -- i.e. admits a strategy that…