Related papers: Truth and collection
On the basis of what I call physico-formalist philosophy of mathematics, I will develop an amended account of the Kantian--Reichenbachian conception of constitutive a priori. It will be shown that the features (attributes, qualities,…
Propositional representation services such as truth maintenance systems offer powerful support for incremental, interleaved, problem-model construction and evaluation. Probabilistic inference systems, in contrast, have lagged behind in…
We present a version of G\"odel's Second Incompleteness Theorem for recursively enumerable consistent extensions of a fixed axiomatizable theory, by incorporating some bi-theoretic version of the derivability conditions. We also argue that…
Peano Arithmetic is known to be provably equivalent to reflection over Elementary Arithmetic. We prove a characterization of Predicative Analysis in the guise of ATR0 in terms of stronger reflection principles.
In a recent paper, Enayat and Le lyk [2024] show that second order arithmetic and countable set theory are not definitionally equivalent. It is well known that these theories are biinterpretable. Thus, we have a pair of natural theories…
This note being devoted to some aspects of the inverse problem of representation theory contains a new insight into it illustrated by two topics. The attention is concentrated on the manner of representation of abstract objects by the…
We compare the expressiveness of two extensions of monadic second-order logic (MSO) over the class of finite structures. The first, counting monadic second-order logic (CMSO), extends MSO with first-order modulo-counting quantifiers,…
We prove some new characterisations of honesty of the perturbed semigroup in Kato's Perturbation Theorem on abstract state spaces via three approaches, namely mean ergodicity of operators, adjoint operators and uniqueness of the perturbed…
A constructive proof of the Goedel-Rosser incompleteness theorem has been completed using the Coq proof assistant. Some theory of classical first-order logic over an arbitrary language is formalized. A development of primitive recursive…
This paper provides a behavioral analysis of conservatism in beliefs. I introduce a new axiom, Dynamic Conservatism, that relaxes Dynamic Consistency when information and prior beliefs "conflict." When the agent is a subjective expected…
We revisit the problem of constructing predictive confidence sets for which we wish to obtain some type of conditional validity. We provide new arguments showing how ``split conformal'' methods achieve near desired coverage levels with high…
We present a general strategy that allows a more flexible method for the construction of fully additive multipartite entanglement monotones than the ones so far reported in the literature of axiomatic entanglement measures. Within this…
Gentzen's 1936 proof of the consistency of Peano Arithmetic was a significant result in the foundations of mathematics. We provide here a modified version of the proof, based on G\"{o}del's reformulation, and including additional details…
In many settings the power of truthful mechanisms is severely bounded. In this paper we use randomization to overcome this problem. In particular, we construct an FPTAS for multi-unit auctions that is truthful in expectation, whereas there…
In this paper we formulate the problem of inference under incomplete information in very general terms. This includes modelling the process responsible for the incompleteness, which we call the incompleteness process. We allow the process…
For Hilbert, the consistency of a formal theory T is an infinite series of statements "D is free of contradictions" for each derivation D and a consistency proof is i) an operation that, given D, yields a proof that D is free of…
Compositional Game Theory is a new, recently introduced model of economic games based upon the computer science idea of compositionality. In it, complex and irregular games can be built up from smaller and simpler games, and the equilibria…
The lambda Pi calculus can be extended with rewrite rules to embed any functional pure type system. In this paper, we show that the embedding is conservative by proving a relative form of normalization, thus justifying the use of the lambda…
We develop a bottom-up approach to truth-value semantics for classical logic of partial terms based on equality and apply it to prove the conservativity of the addition of partial description and partial selection functions, independently…
In this paper, we investigate the extent to which knowledge compilation can be used to improve inference from propositional weighted bases. We present a general notion of compilation of a weighted base that is parametrized by any…