Related papers: A note on the consistency operator
At the beginning of a dynamic game, players may have exogenous theories about how the opponents are going to play. Suppose that these theories are commonly known. Then, players will refine their first-order beliefs, and challenge their own…
We give necessary and sufficient geometric conditions for a theory definable in an o-minimal structure to interpret a real closed field. The proof goes through an analysis of thorn-minimal types in super-rosy dependent theories of finite…
The Majority is Stablest Theorem has numerous applications in hardness of approximation and social choice theory. We give a new proof of the Majority is Stablest Theorem by induction on the dimension of the discrete cube. Unlike the…
This paper introduces statistical order convergence and its pointwise variant for sequences of order bounded operators between Riesz spaces. We establish fundamental properties: uniqueness of the limit, stability under lattice operations,…
Quantum theory provides a significant example of two intermingling hallmarks of science: the ability to consistently combine physical systems and study them compositely, and the power to extract predictions in the form of correlations. A…
Our approach is basically a coherence approach, but we avoid the well-known pitfalls of coherence theories of truth. Consistency is replaced by reliability, which expresses support and attack, and, in principle, every theory (or agent,…
We rewrite simplicially the standard definitions of a complete first order theory, a model of it, and various characterisations of stability of a complete first order theory. In our reformulations the simplicial language replaces the…
The multiplicative theory of a set of numbers (which could be natural, integer, rational, real or complex numbers) is the first-order theory of the structure of that set with (solely) the multiplication operation (that set is taken to be…
We prove that a theory $T$ has stable forking if and only if $T^\mathrm{eq}$ has stable forking.
This paper provides a complete suite of axioms for a version of set theory that I call Explication. Explication borrows from the two most prominent existing systems of set theory. Explication starts with class variables. After several…
Theoretical analysis proves that human survivability is dominated by an unusual physical, rather than biological, mechanism, which yields an exact law. The law agrees with all experimental data, but, contrary to existing theories, it is the…
A new notion of independence relation is given and associated to it, the class of flat theories, a subclass of strong stable theories including the superstable ones is introduced. More precisely, after introducing this independence…
We make two contributions to the study of theory combination in satisfiability modulo theories. The first is a table of examples for the combinations of the most common model-theoretic properties in theory combination, namely stable…
Most natural languages have a predominant or fixed word order. For example in English the word order is usually Subject-Verb-Object. This work attempts to explain this phenomenon as well as other typological findings regarding word order…
We show that if a numerical method is posed as a sequence of operators acting on data and depending on a parameter, typically a measure of the size of discretization, then consistency, convergence and stability can be related by a…
The kinetic energy operator of a quantum particle with position dependent mass and the associated ordering ambiguity is revisited. We introduce a new form of this operator which is a continues or discreet superposition of the acceptable…
Transparency is a fundamental requirement for decision making systems when these should be deployed in the real world. It is usually achieved by providing explanations of the system's behavior. A prominent and intuitive type of explanations…
We prove that in a countable theory T fully stable over a predicate P, any complete set A has the existence property. This means that A can be extended to a model of T without changing the P-part. In particular, T has the Gaifman property:…
In order to develop efficient tools for automated reasoning with inconsistency (theorem provers), eventually making Logics of Formal inconsistency (LFI) a more appealing formalism for reasoning under uncertainty, it is important to develop…
In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…