Related papers: On certain constructive predicate calculus
The logic of constant domains is intuitionistic logic extended with the so-called forall-shift axiom, a classically valid statement which implies the excluded middle over decidable formulas. Surprisingly, this logic is constructive and so…
We present a calculus providing a Curry-Howard correspondence to classical logic represented in the sequent calculus with explicit structural rules, namely weakening and contraction. These structural rules introduce explicit erasure and…
In a recent paper, Herbelin developed a calculus dPA$^\omega$ in which constructive proofs for the axioms of countable and dependent choices could be derived via the encoding of a proof of countable universal quantification as a stream of…
We investigate a hierarchy of arithmetical structures obtained by a transfinite addition of a canonic universal predicate, where the canonic universal predicate for M is defined as a minimum universal predicate for M in terms of…
Neither the classical nor intuitionistic logic traditions are perfectly-aligned with the purpose of reasoning about computation, in that neither tradition can permit unconstrained recursive definitions without inconsistency: recursive…
In this paper we investigate the Curry-Howard correspondence for constructive modal logic in light of the gap between the proof equivalences enforced by the lambda calculi from the literature and by the recently defined winning strategies…
We report first steps towards elucidating the relationship between contextuality, measurement-based quantum computation (MBQC) and the non-classical logic of a topos associated with the computation. We show that, in a class of MBQC,…
Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a…
Argumentation is the process of constructing arguments about propositions, and the assignment of statements of confidence to those propositions based on the nature and relative strength of their supporting arguments. The process is modelled…
Calculational abstract interpretation, long advocated by Cousot, is a technique for deriving correct-by-construction abstract interpreters from the formal semantics of programming languages. This paper addresses the problem of deriving…
We shall construct by ordinary recursion method subsets to the set $D$ of G\"odel numbers of the sentences of a language $\mathcal L$. That language is formed by sentences of a fully interpreted formal language $L$, called an MA language,…
Debates concerning philosophical grounds for the validity of classical and intuitionistic logics often have the very nature of logical proofs as one of the main points of controversy. The intuitionist advocates for a strict notion of…
Computability logic is a formal theory of computational tasks and resources. Its formulas represent interactive computational problems, logical operators stand for operations on computational problems, and validity of a formula is…
In this paper, we argue that formal systems of first order Arithmetic that admit Goedelian undecidable propositions validly are abnormally non-constructive. We argue that, in such systems, the strong representation of primitive recursive…
Pure type systems arise as a generalisation of simply typed lambda calculus. The contemporary development of mathematics has renewed the interest in type theories, as they are not just the object of mere historical research, but have an…
At the onset of quantum mechanics, it was argued that the new theory would entail a rejection of classical logic. The main arguments to support this claim come from the non-commutativity of quantum observables, which allegedly would…
Cirquent calculus is a novel proof theory permitting component-sharing between logical expressions. Using it, the predecessor article "Elementary-base cirquent calculus I: Parallel and choice connectives" built the sound and complete…
The AMR (Abstract Meaning Representation) formalism for representing meaning of natural language sentences was not designed to deal with scope and quantifiers. By extending AMR with indices for contexts and formulating constraints on these…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
In a forthcoming book, professional computer scientist and physicist Paul Budnik presents an exposition of classical mathematical theory as the backdrop to an elegant thesis: we can interpret any model of a formal system of Peano Arithmetic…