Related papers: Coinductive Validity
We introduce a new logic that combines Adjoint Logic with Graded Necessity Modalities. This results in a very expressive system capable of controlling when and how structural rules are used. We give a sequent calculus, natural deduction,…
It is known that intuitionistic Kripke semantics can be generalized so that it can treat arbitrary propositional connectives characterized by truth functions. We extend this generalized Kripke semantics to first-order logic, and study how…
Null Hypothesis Statistical Testing is a dominant framework for conducting statistical analysis across the sciences. There remains considerable debate as to whether, and under what circumstances, evidence can be said to be confirmatory of a…
We offer the proofs that complete our article introducing the propositional calculus called semi-intuitionistic logic with strong negation.
Goedel's results have had a great impact in diverse fields such as philosophy, computer sciences and fundamentals of mathematics. The fact that the rule of mathematical induction is contradictory with the rest of clauses used by Goedel to…
In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results
Coinductive reasoning about infinitary structures such as streams is widely applicable. However, practical frameworks for developing coinductive proofs and finding reasoning principles that help structure such proofs remain a challenge,…
Theorem provers are tools that help users to write machine readable proofs. Some of this tools are also interactive. The need of such softwares is increasing since they provide proofs that are more certified than the hand written ones. Agda…
Classical logic is embedded into constructive logic, through a definition of the classical connectives and quantifiers in terms of the constructive ones.
We formulate the Hauptvermutung of Causal Set Theory in two mathematically well-defined but different ways one of which turns out to be wrong and the other one turns out to be true. A further result is that the Hauptvermutung is true if we…
This article contains a proposal to add coinduction to the computational apparatus of natural language understanding. This, we argue, will provide a basis for more realistic, computationally sound, and scalable models of natural language…
This short note proposes a symbolic approach for representing and reasoning about quantum circuits using complex, vector or matrix-valued Boolean expressions. A major benefit of this approach is that it allows us to directly borrow the…
We study a new proof principle in the context of constructive Zermelo-Fraenkel set theory based on what we will call "non-deterministic inductive definitions". We give applications to formal topology as well as a predicative justification…
A quantum-like description of human decision process is developed, and a heuristic argument supporting the theory as sound phenomenology is given. It is shown to be capable of quantitatively explaining the conjunction fallacy in the same…
The paper contains an alternative proof of M. Kontsevich Formality Theorem.
We show the functional completeness for the connectives of the non-trivial negation inconsistent logic C by using a well-established method implementing purely proof-theoretic notions only. Firstly, given that C contains a strong negation,…
This paper studies the proof of Collatz conjecture for some set of sequence of odd numbers with infinite number of elements. These set generalized to the set which contains all positive odd integers. This extension assumed to be the proof…
We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.
Well-known principles of induction include monotone induction and different sorts of non-monotone induction such as inflationary induction, induction over well-founded sets and iterated induction. In this work, we define a logic formalizing…
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…