In several recent articles, we have shown how such totality conditions are related to both generalizations and boundary-case exceptions for the Second Incompleteness Theorem. For instance, our article [2] showed how essentially all axiom systems recognizing addition and multiplication as “total” functions are unable to prove a theorem affirming their semantic tableaux consistency. In contrast, ...

We consider a family of sequent systems with “well-behaved” logical rules in which the cut rule and/or the identity-axiom are not present. We provide a semantic characterization of the logics induced by these systems in the form of non-deterministic three-valued or four-valued matrices. The semantics is used to study some important proof-theoretic properties of these systems. These results shed...

“ba:y?d” as a persian lexeme is interwoven with modality, a semantic category and therefore has a complicated and thought- provoking semantic nature. this paper uses evidence from persian to investigate the usage of this lexeme and some of its semantic and pragmatic aspects in this language. the results indicate that this lexical category can convey a wide range of modal meanings in different c...

In recent publications Alain Connes [1] and John Barrett [2] proposed to change the KO-dimension of the internal space of the standard model in its noncommutative representation [3] from zero to six. This apparently minor modification allowed to resolve the fermion doubling problem [4], and the introduction of Majorana mass terms for the right-handed neutrino. The price which had to be paid was...

A non-trivial, transitive and reflexive binary relation on the set of lotteries satisfying independence that also satisfies any two of the following three axioms satisfies the third: completeness, Archimedean and mixture continuity (Dubra (2011)). This paper generalizes Dubra’s result in two ways: First, by replacing independence with a weaker betweenness axiom. Second, by replacing independenc...

philosophers from one hand take the “al-vahed” axiom for granted, and on the other hand, they assume that the almighty to be of absolute power. now the question is whether: this is at odds with the “al- vahed” axiom? how can we accept at the same time the absolute power of the almighty and the “al-vahed” axiom? we should say here: majority of philosophers, mystics and kalam specialists have cla...

We present a set of axioms that justify the use of belief functions to quantify the beliefs held by an agent Y at time t and based on Y's evidential corpus. It is essentially postulated that degrees of belief are quantified by a function in [0,1] that give the same degrees of beliefs to subsets that represent the same propositions according to Y's evidential corpus. We derive the impact of the ...

The article is continuation of [2] and [1], and the goal of it is show that Zermelo theorem (every set has a relation which well orders it proposition (26)) and axiom of choice (for every non-empty family of non-empty and separate sets there is set which has exactly one common element with arbitrary family member proposition (27)) are true. It is result of the Tarski’s axiom A introduced in [5]...

We give here the first examples of C structurally stable maps in manifolds of dimension greater than one that are not diffeomorphisms nor expanding. It is shown that an Axiom A endomorphism all of whose basic pieces are expanding or attracting is C stable. A necessary condition for the existence of such examples is also given.

We revise our ‘Physical Traces’ paper [Abramsky and Coecke CTCS‘02] in the light of the results in [Abramsky and Coecke LiCS‘04]. The key fact is that the notion of a strongly compact closed category allows abstract notions of adjoint, bipartite projector and inner product to be defined, and their key properties to be proved. In this paper we improve on the definition of strong compact closure ...