Related papers: Classical consequences of continuous choice princi…
We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second G\"odel incompleteness theorem to stably…
A fundamental question is whether Turing machines can model all reasoning processes. We introduce an existence principle stating that the perception of the physical existence of any Turing program can serve as a physical causation for the…
We improve the answer to the question: what set of excluded middles for propositional variables in a formula suffices to prove the formula in intuitionistic propositional logic whenever it is provable in classical propositional logic.
A fundamental question in causal inference is whether it is possible to reliably infer manipulation effects from observational data. There are a variety of senses of asymptotic reliability in the statistical literature, among which the most…
We investigate cut-elimination and cut-simulation in impredicative (higher-order) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus for an impredicative logic -- in our case a sequent calculus for…
We introduce and study single-conclusioned nested sequent calculi for a broad class of intuitionistic multi-modal logics known as "intuitionistic grammar logics (IGLs)." These logics serve as the intuitionistic counterparts of classical…
The material conditional has long been charged with paradox. Defined truth-functionally, it renders true any conditional whose antecedent is false or consequent true -- hence, seemingly absurd statements such as `If unicorns exist, then…
We continue our work on the model theory of free lattices, solving two of the main open problems from our first paper on the subject. Our main result is that the universal (existential) theory of infinite free lattices is decidable. Our…
This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argumentative-consequence relation taking into account the existence of consistent arguments in favor of a conclusion and the…
In much discussed work Artemov has recently shown that, for $\mathrm{PA}$, the consistency schema admits a form of uniform verification via selector proofs, despite the unprovability of the corresponding uniform consistency sentence…
In the context of continuous first-order logic, special attention is often given to theories that are somehow continuous in an 'essential' way. A common feature of such theories is that they do not interpret any infinite discrete…
The Necessary Maximality Principle for c.c.c. forcing asserts that any statement about a real in a c.c.c. extension that could become true in a further c.c.c. extension and remain true in all subsequent c.c.c. extensions, is already true in…
We provide, for any regular uncountable cardinal $\kappa$, a new argument for Pincus' result on the consistency of $\mathrm{ZF}$ with the higher dependent choice principle $\mathrm{DC}_{<\kappa}$ and the ordering principle in the presence…
We show that Dependent Choice is a sufficient choice principle for developing the basic theory of proper forcing, and for deriving generic absoluteness for the Chang model in the presence of large cardinals, even with respect to…
Between the two dominant schools of thought in statistics, namely, Bayesian and classical/frequentist, a main difference is that the former is grounded in the mathematically rigorous theory of probability while the latter is not. In this…
We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and…
Goodstein sequences are numerical sequences in which a natural number m, expressed as the complete normal form to a given base a, is modified by increasing the value of the base a by one unit and subtracting one unit from the resulting…
Classical evaluations of configurations of intertwined quantum contexts induce relations, such as true-implies-false, true-implies-true, but also nonseparability among the input and output terminals. When combined, these exploitable…
We advance a general theory of coherent preference that surrenders restrictions embodied in orthodox doctrine. This theory enjoys the property that any preference system admits extension to a complete system of preferences, provided it…
If $L$ is a relational language, then an $L$-structure ${\mathbb X}=\langle X,\bar \rho \rangle$ is reversible iff there is no interpretation $\bar \sigma \varsubsetneq \bar \rho$ such that the structures $\langle X,\bar \sigma \rangle$ and…