Related papers: On Classical Determinate Truth
As it is well known, classical mechanics consists of several basic features like determinism, reductionism, completeness of knowledge and mechanicism. In this article the basic assumptions are discussed which underlie those features. It is…
A canonical result in model theory is the homomorphism preservation theorem (h.p.t.) which states that a first-order formula is preserved under homomorphisms iff it is equivalent to an existential-positive formula, standardly proved via a…
Propositional type theory, first studied by Henkin, is the restriction of simple type theory to a single base type that is interpreted as the set of the two truth values. We show that two constants (falsity and implication) suffice for…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
Many-valued models generalise the structures from classical model theory by defining truth values for a model with an arbitrary algebra. Just as algebraic varieties provide semantics for many non-classical propositional logics, models…
In this paper we show how to introduce a conditional to Kripke's theory of truth that respects the deduction theorem for the consequence relation associated with the theory. To this effect we develop a novel supervaluational framework,…
Mathematicians still use Naive Set Theory when generating sets without danger of producing any contradiction. Therefore their working method can be considered as a consistent inference system with an experience of over 100 years. My…
The field of proof-theoretic semantics (P-tS) offers an alternative approach to meaning in logic that is based on inference and argument (rather than truth in a model). It has been successfully developed for various logics; in particular,…
By a well-known result of Kotlarski, Krajewski, and Lachlan (1981), first-order Peano arithmetic $PA$ can be conservatively extended to the theory $CT^{-}[PA]$ of a truth predicate satisfying compositional axioms, i.e., axioms stating that…
One of the key challenges when looking for the causes of a complex event is to determine the causal status of factors that are neither individually necessary nor individually sufficient to produce that event. In order to reason about how…
We prove the algorithmic canonicity of two classes of $\mu$-inequalities in a constructive meta-theory of normal lattice expansions. This result simultaneously generalizes Conradie and Craig's canonicity for $\mu$-inequalities based on a…
We give a definition of finitary type theories that subsumes many examples of dependent type theories, such as variants of Martin-L\"of type theory, simple type theories, first-order and higher-order logics, and homotopy type theory. We…
We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic…
Intuitively, the more powerful a theory is, the greater the variety and quantity of ideas can be expressed through its formal language. Therefore, when comparing two theories concerning the same subject, it seems only reasonable to compare…
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.…
In this paper we consider a type system with a universal type $\omega$ where any term (whether open or closed, $\beta$-normalising or not) has type $\omega$. We provide this type system with a realisability semantics where an atomic type is…
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…
This paper develops a categorical framework to clarify the relationship between the completeness and compactness theorems in classical first-order logic. Rather than claiming that different model constructions yield naturally isomorphic…
We present a unified categorical treatment of completeness theorems for several classical and intuitionistic infinitary logics with a proposed axiomatization. This provides new completeness theorems and subsumes previous ones by G\"odel,…
Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces and homotopy invariant fixed point theory. We show that in many cases,…