Related papers: On Defining 'I' "I logy"
We investigate the isomorphism problem in the setting of definable sets (equivalent to sets with atoms): given two definable relational structures, are they related by a definable isomorphism? Under mild assumptions on the underlying…
The dual character of invariance under transformations and definability by some operations has been used in classical work by for example Galois and Klein. Following Tarski, philosophers of logic have claimed that logical notions themselves…
Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…
Here, by introducing a version of "Unexpected hanging paradox" we try to open a new way and a new explanation for paradoxes, similar to liar paradox. Also, we will show that we have a semantic situation which no syntactical logical system…
We discuss the question of if and how undecidability might be translatable into physics, in particular with respect to prediction and description, as well as to complementarity games.
We use a generalization of a construction by Ziegler to show that for any field $F$ and any countable collection of countable subsets $A_i \subseteq F, i \in \calI \subset \Z_{>0}$ there exist infinitely many fields $K$ of arbitrary…
This paper is a survey of a large number of informal definitions of ``intelligence'' that the authors have collected over the years. Naturally, compiling a complete list would be impossible as many definitions of intelligence are buried…
There are various non-equivalent definitions of locality. Three of them, impossibility of instantaneous communication, impossibility of action-at-a-distance, and impossibility of faster-than-light travel, while not fully implying each…
In order to design strong paradigms for isolating lexical access and semantics, we need to know what a word is. Surprisingly few linguists and philosophers have a clear model of what a word is, even though words impact basically every…
As is known, AGI (Artificial General Intelligence), unlike AI, should operate with meanings. And that's what distinguishes it from AI. Any successful AI implementations (playing chess, unmanned driving, face recognition etc.) do not operate…
The definition is a common form of human expert knowledge, a building block of formal science and mathematics, a foundation for database theory and is supported in various forms in many knowledge representation and formal specification…
The paper proposes a new type of negation in multi-valued logics, providing a different way to answer the following question: what does it mean that some object language formula does not have a given truth-value. Along the way, the paper…
In the knowledge engineering community "ontology" is usually defined in the tradition of Gruber as an "explicit specification of a conceptualization". Several variations of this definition exist. In the paper we argue that (with one notable…
This paper presents rules of inference for a binary quantifier $I$ for the formalisation of sentences containing definite descriptions within intuitionist positive free logic. $I$ binds one variable and forms a formula from two formulas.…
Contrary to popular misconception, the question in the title is far from simple. It involves sets of numbers on the first level, sets of sets of numbers on the second level, and so on, endlessly. The infinite hierarchy of the levels…
A fundamental problem in artificial intelligence is that nobody really knows what intelligence is. The problem is especially acute when we need to consider artificial systems which are significantly different to humans. In this paper we…
Even though every mathematician knows intuitively what it means to "simplify" a mathematical expression, there is still no universally accepted rigorous mathematical definition of "simplify". In this paper, we shall give a simple and…
Limit can be defined by two axioms: 1. Strict inequality between limits implies, ultimately, strict inequality between functions. 2. For constant functions limit is trivial. How can basic results on convergence be derived from these axioms?…
We discuss the problem of defining a logic for analogical reasoning, and sketch a solution in the style of the semantics for Counterfactual Conditionals, Preferential Structures, etc.
A typical kind of question in mathematical logic is that for the necessity of a certain axiom: Given a proof of some statement $\phi$ in some axiomatic system $T$, one looks for minimal subsystems of $T$ that allow deriving $\phi$. In…