Related papers: Varieties of truth definitions
The first contribution of this paper is the presentation of a Pavelka - like formulation of possibilistic logic in which the language is naturally enriched by two connectives which represent negation (eg) and a new type of conjunction…
Cie\'sli\'nski asked whether compositional truth theory with the additional axiom that all propositional tautologies are true is conservative over Peano Arithmetic. We provide a partial answer to this question, showing that if we…
We analyze the informal notion of truth and conclude that it can be formalized in essentially two distinct ways: constructively, in terms of provability, or classically, as a hierarchy of concepts which satisfy Tarski's biconditional in…
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…
Our main result (Theorem A) shows the incompleteness of any consistent sequential theory T formulated in a finite language such that T is axiomatized by a collection of sentences of bounded quantifier-alternation-depth. Our proof employs an…
We conceptualize explainability in terms of logic and formula size, giving a number of related definitions of explainability in a very general setting. Our main interest is the so-called special explanation problem which aims to explain the…
A true lie is a lie that becomes true when announced. In a logic of announcements, where the announcing agent is not modelled, a true lie is a formula (that is false and) that becomes true when announced. We investigate true lies and other…
In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications, in a similar spirit than a set of proof trees. The main…
A model of knowledge representation is described in which propositional facts and the relationships among them can be supported by other facts. The set of knowledge which can be supported is called the set of cognitive units, each having…
We consider extensions of the language of Peano arithmetic by transfinitely iterated truth definitions satisfying uniform Tarskian biconditionals. Without further axioms, such theories are known to be conservative extensions of the original…
Recently, Artemov [4] offered the notion of constructive consistency for Peano Arithmetic and generalized it to constructive truth and falsity in the spirit of Brouwer-Heyting-Kolmogorov semantics and its formalization, the Logic of Proofs.…
We consider the fragment F of first order arithmetic in which quantification is restricted to ''for all but finitely many.'' We show that the integers form an F-elementary substructure of the real numbers. Consequently, the F-theory of…
It is generally accepted that the incompleteness of first-order number theory (PA) is established by an application of Godel's proof. This paper shows that the arithmetization of the syntax of PA implies that the hypothesised class of PA…
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,…
Using the theory of Kolmogorov complexity the notion of facticity {\phi}(x) of a string is defined as the amount of self-descriptive information it contains. It is proved that (under reasonable assumptions: the existence of an empty machine…
A formula $\phi$ is called \emph{$n$-provable} in a formal arithmetical theory $S$ if $\phi$ is provable in $S$ together with all true arithmetical $\Pi_{n}$-sentences taken as additional axioms. While in general the set of all $n$-provable…
In this paper we prove Chaitin's ``heuristic principle'', {\it the theorems of a finitely-specified theory cannot be significantly more complex than the theory itself}, for an appropriate measure of complexity. We show that the measure is…
Given any collection F of computable functions over the reals, we show that there exists an algorithm that, given any L_F-sentence \varphi containing only bounded quantifiers, and any positive rational number \delta, decides either "\varphi…
One of the greatest problems in philosophy is that of meaning. The turning point in thinking on meaning was Tarski's definition of truth, and the rapid development of logical semantics and model theory was a consequence of this achievement.…
We provide a sound and complete proof system for an extension of Kleene's ternary logic to predicates. The concept of theory is extended with, for each function symbol, a formula that specifies when the function is defined. The notion of…