相关论文: On Defining 'I' "I logy"
The paper adresses the problem of reasoning with ambiguities. Semantic representations are presented that leave scope relations between quantifiers and/or other operators unspecified. Truth conditions are provided for these representations…
The method K\"urbis used to formalise definite descriptions with a binary quantifier I, such that I$x[F,G]$ indicates `the F is G', is examined and improved upon in this work. K\"urbis first looked at I in intuitionistic logic and its…
For any first order theory T we construct a Boolean valued model M, in which precisely the T--provable formulas hold, and in which every (Boolean valued) subset which is invariant under all automorphisms of M is definable by a first order…
When a decision, such as the approval or denial of a bank loan, is delegated to a computer, an explanation of that decision ought to be given with it. This ethical need to explain the decisions leads to the search for a formal definition of…
In this paper, we define an intuitionistic version of Computation Tree Logic. After explaining the semantic features of intuitionistic logic, we examine how these characteristics can be interesting for formal verification purposes.…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
Many mathematical statements have the following form. If something is true for all finite subsets of an infinite set $I$, then it is true for all of $I$. This paper describes some old and new results on infinite sets of linear and…
Similarity metric which is not positive definite, and present a general theorem which provides a large family of similarity metrics which are positive definite.
Ordinary first-order logic has the property that two formulas \phi and \psi have the same meaning in a structure if and only if the formula ``\phi iff \psi'' is true in the structure. We prove that independence-friendly logic does not have…
We look at characterizing which formulas are expressible in rich decidable logics such as guarded fixpoint logic, unary negation fixpoint logic, and guarded negation fixpoint logic. We consider semantic characterizations of definability, as…
There is some ambiguity of what agile means in both research and practice. Authors have suggested a diversity of different definitions, through which it is difficult to interpret what agile really is. The concept, however, exists in its…
In logic there is a clear concept of what constitutes a proof and what not. A proof is essentially defined as a finite sequence of formulae which are either axioms or derived by proof rules from formulae earlier in the sequence.…
This article discusses the logical errors in the liar paradox, G\"odel's incompleteness theorems, Russell's paradox, and the halting problem. In order to avoid these errors, a redefinition of logic has been presented, which is concluded as…
We define an equivalence relation on propositions and a proof system where equivalent propositions have the same proofs. The system obtained this way resembles several known non-deterministic and algebraic lambda-calculi.
We study whether Artificial General Intelligence (AGI) admits a coherent theoretical definition that supports absolute claims of existence, robustness, or self-verification. We formalize AGI axiomatically as a distributional,…
Definition Modeling, the task of generating definitions, was first proposed as a means to evaluate the semantic quality of word embeddings-a coherent lexical semantic representations of a word in context should contain all the information…
In 1932, G\"odel proved that there is no finite semantics for intuitionistic logic. We consider all fragments of intuitionistic logic and check in each case whether a finite semantics exists. We may fulfill a didactic goal, as little logic…
Two different definitions of the Artificial Intelligence concept have been proposed in papers [1] and [2]. The first definition is informal. It says that any program that is cleverer than a human being, is acknowledged as Artificial…
Defining artificial intelligence (AI) is a persistent challenge, often muddied by technical ambiguity and varying interpretations. Commonly used definitions heavily emphasize technical properties of AI but neglect the human purpose of it.…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…