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Published at December 4

A Cut-free, Sound and Complete Russellian Theory of Definite Descriptions

cs.LO

math.LO

Released Date: December 4, 2024

Authors: Andrzej Indrzejczak¹, Nils Kürbis¹

Aff.: ¹Department of Logic, University of Lodz, Poland

Arxiv: http://arxiv.org/pdf/2412.03251v1

$M,v\models P^{n}(t_{1},...,t_{n})$	iff	$\langle v(t_{1}),\ldots,v(t_{n})\rangle\in I(P^{n})$
$M,v\models t_{1}=t_{2}$	iff	$v(t_{1})=v(t_{2})$
$M,v\models(\lambda x\psi)t$	iff	$M,v^{x}_{o}\models\psi$ , where $o=v(t)$
$M,v\models(\lambda x\psi)\imath y\varphi$	iff	there is an $o\in D$ such that $M,v^{x}_{o}\models\psi$ , and
		$M,v^{x}_{o}\models\varphi[y/x]$ , and for any $y$ -variant $v^{\prime}$ of $v^{x}_{o}$ ,
		if $M,v^{\prime}\models\varphi$ , then $v^{\prime}(y)=o$
$M,v\models\neg\varphi$	iff	$M,v\not\models\varphi$ ,
$M,v\models\varphi\land\psi$	iff	$M,v\models\varphi$ and $M,v\models\psi$ ,
$M,v\models\forall x\varphi$	iff	$M,v^{x}_{o}\models\varphi$ , for all $o\in D$ .