Related papers: Implicational Completeness
We present a propositional logic with fundamental probabilistic semantics, in which each formula is given a real measure in the interval $[0,1]$ that represents its degree of truth. This semantics replaces the binarity of classical logic,…
We present a standard calculus for logical grounding based on well-established grounding principles [Schnieder, 2011, Fine, 2012, Correia, 2014, Correia, 2024] and provide a very direct characterisation of the provable grounding claims…
This paper gives a detailed account of the relationship between (a variant of) the call-by-value lambda calculus and linear logic proof nets. The presentation is carefully tuned in order to realize a strong bisimulation between the two…
We discuss proving correctness and completeness of definite clause logic programs. We propose a method for proving completeness, while for proving correctness we employ a method which should be well known but is often neglected. Also, we…
We give a reframing of Godel's first and second incompleteness theorems that applies even to some undefinable theories of arithmetic. The usual Hilbert-Bernays provability conditions and the diagonal lemma are replaced by a more direct…
We present a necessary and sufficient condition for a Boolean algebra to carry a finitely additive measure.
We designed a superposition calculus for a clausal fragment of extensional polymorphic higher-order logic that includes anonymous functions but excludes Booleans. The inference rules work on $\beta\eta$-equivalence classes of…
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
An exposition of smooth infinitesimal analysis, which is a way to do calculus with nilsquare infinitesimals, is given.
The algorithm to compute theory prime implicates, a generalization of prime implicates, in propositional logic has been suggested in \cite{Marquis}. In this paper we have extended that algorithm to compute theory prime implicates of a…
We give a detailed account of the classical Van Kampen method for computing presentations of fundamental groups of complements of complex algebraic curves, and of a variant of this method, working with arbitrary projections (even with…
We present a completeness result for the implicit fragment of justification stit logic. Although this fragment allows for no strongly complete axiomatization, we show that a restricted form of strong completeness (subsuming weak…
We discuss the application of the determinantal method to the proof of the Riemann hypothesis. We start from the fact that, if a certain doubly infinite set of determinants are all positive, then the hypothesis is true. This approach…
We introduce a new criterion which if satisfied implies the Riemann hypothesis.
This paper obtains a completeness result for inequational reasoning with applicative terms without variables in a setting where the intended semantic models are the full structures, the full type hierarchies over preorders for the base…
We improve the answer to the question: what set of excluded middles for propositional variables in a formula suffices to prove the formula in intuitionistic propositional logic whenever it is provable in classical propositional logic.
We build a variant of Collatz Conjecture for polynomials over $\mathbb{F}_2$ and we prove that it is solved. By the way, we give several examples.
In order to prove that the P of problems is different to the NP class, we consider the satisfability problem of propositional calculus formulae, which is an NP-complete problem. It is shown that, for every search algorithm A, there is a set…
In this paper we give two theorems from the Propositional Calculus of the Boolean Logic with their consequences and applications and we prove them axiomatically.
This Note revisits the Leibnitz integral calculus method based on differentiation under the integral sign with respect to a parameter either already existing or introduced ad hoc. Through several cases exemplifying the method, it is shown…