Related papers: ZF*-Extensionality interprets full ZF
Epistemic logic programs constitute an extension of the stable models semantics to deal with new constructs called subjective literals. Informally speaking, a subjective literal allows checking whether some regular literal is true in all…
In this paper, we study the weighted difference substitutions from geometrical views. First, we give the geometric meanings of the weighted difference substitutions, and introduce the concept of convergence of the sequence of substitution…
It is well known that ZFC, despite its usefulness as a foundational theory for mathematics, has two unwanted features: it cannot be written down explicitly due to its infinitely many axioms, and it has a countable model due to the…
We show that in Zermelo-Fraenkel Set Theory without the Axiom of Choice a surjectively modified continuum function $\theta(\kappa)$ can take almost arbitrary values for all infinite cardinals. This choiceless version of Easton's Theorem is…
A result of Kaufmann shows that if $L_\alpha$ is countable, admissible and satisfies $\Pi_n\textsf{-Collection}$, then $\langle L_\alpha, \in \rangle$ has a proper $\Sigma_{n+1}$-elementary end extension. This paper investigates to what…
We examine what happens if we replace ZFC with a localistic/relativistic system, LZFC, whose central new axiom, denoted by $Loc({\rm ZFC})$, says that every set belongs to a transitive model of ZFC. LZFC consists of $Loc({\rm ZFC})$ plus…
We review a minimum set of notions from our previous paper on structural properties of SAT at arXiv:0802.1790 that will allow us to define and discuss the "complete internal independence" of a decision problem. This property is strictly…
LF is a dependent type theory in which many other formal systems can be conveniently embedded. However, correct use of LF relies on nontrivial metatheoretic developments such as proofs of correctness of decision procedures for LF's…
Let F be a field complete for a real valuation. It is a standard result in valuation theory that a finite extension of F admits a valuation basis if and only if it is without defect. We show that even otherwise, one can construct bases in…
This paper offers an approach to extensible knowledge representation and reasoning for a family of formalisms known as Description Logics. The approach is based on the notion of adding new concept constructors, and includes a heuristic…
This is a further explanation of a new and simple renormalization approach recently proposed by the author (hep-th/9708104, Ref. [1], that is somewhat sketchy) for any ordinary QFT (whether renormalizable or not) in any spacetime dimension.…
This paper contains an alternate proof of the Schanuel Nullstellensatz for Zilber's Pseudoexponentiation. Furthermore, in an algebraically closed exponential field whose exponential map is surjective with standard kernel, this property…
We introduce extensions by rules of the extensional level of the Minimalist Foundation which turn out to be equivalent to constructive and classical axiomatic set theories.
We define a notion of general uniform interpolant, generalizing the notions of cover and of uniform interpolant and identify situations in which symbol elimination can be used for computing general uniform interpolants. We investigate the…
We present a new method for completing higher derivative corrections for theories that exhibit duality symmetries under reduction. This proposal is based on the observation that duality symmetry in the reduced theory highly constrains the…
Motivated by applications in declarative data analysis, we study $\mathit{Datalog}_{\mathbb{Z}}$---an extension of positive Datalog with arithmetic functions over integers. This language is known to be undecidable, so we propose two…
We outline the current status of the differential expansion (DE) of colored knot polynomials i.e. of their $Z$--$F$ decomposition into representation-- and knot--dependent parts. Its existence is a theorem for HOMFLY-PT polynomials in…
In this work we provide alternative formulations of the concepts of lambda theory and extensional theory without introducing the notion of substitution and the sets of all, free and bound variables occurring in a term. We also clarify the…
We discuss generalizations of the recent theorem by Dafermos (hep-th/0403033) forbidding a certain class of naked singularities in the spherical collapse of a scalar field. Employing techniques similar to the ones Dafermos used, we consider…
Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…