Related papers: Cyclic and Inductive Calculi are equivalent
The set of integer number lists with finite length, and the set of binary trees with integer labels are both countably infinite. Many inductively defined types also have countably many elements. In this paper, we formalize the syntax of…
Defeasible statements are statements that are likely, or probable, or usually true, but may occasionally be false. Plausible reasoning makes conclusions from statements that are either facts or defeasible statements without using numbers.…
The aim of this paper is to offer the first systematic exploration and definition of equivalent causal models in the context where both models are not made up of the same variables. The idea is that two models are equivalent when they agree…
The notion of clause set cycle abstracts a family of methods for automated inductive theorem proving based on the detection of cyclic dependencies between clause sets. By discerning the underlying logical features of clause set cycles, we…
By means of the mathematical analysis theory, inequality theory, mathematical induction and the dimension reduction method, under the proper hypotheses, we establish the following cyclic inequalities: \[\sum_{i=1}^{n}…
We show that Morley's theorem on the number of countable models of a countable first-order theory becomes an undecidable statement when extended to second-order logic. More generally, we calculate the number of equivalence classes of…
The logic of bunched implication BI provides a framework for reasoning about resource composition and forms the basis for an assertion language of separation logic which is used to reason about software programs. Propositional BI is…
First-order multiplicative intuitionistic linear logic (MILL1) can be seen as an extension of the Lambek calculus. In addition to the fragment of MILL1 which corresponds to the Lambek calculus (of Moot & Piazza 2001), I will show fragments…
We prove a conjecture of Dukes and Herke concerning the possible orders of a basis for the cyclic group Z_n, namely : For each k \in N there exists a constant c_k > 0 such that, for all n \in N, if A \subseteq Z_n is a basis of order…
Reasoning about actual causes of observed effects is fundamental to the study of rationality. This important problem has been studied since the time of Aristotle, with formal mathematical accounts emerging recently. We live in a world where…
The sequent calculus is a formalism for proving validity of statements formulated in First-Order Logic. It is routinely used in computer science modules on mathematical logic. Formal proofs in the sequent calculus are finite trees obtained…
In this article we relate a family of methods for automated inductive theorem proving based on cycle detection in saturation-based provers to well-known theories of induction. To this end we introduce the notion of clause set cycles -- a…
We consider an example of four valued semantics partially inspired by quantum computations and negation-like operations occurred therein. In particular we consider a representation of so called square root of negation within this four…
Much of scientific data is collected as randomized experiments intervening on some and observing other variables of interest. Quite often, a given phenomenon is investigated in several studies, and different sets of variables are involved…
Two factorizations of a permutation into products of cycles are equivalent if one can be obtained from the other by repeatedly interchanging adjacent disjoint factors. This paper studies the enumeration of equivalence classes under this…
We introduce a functional calculus with simple syntax and operational semantics in which the calculi introduced so far in the Curry-Howard correspondence for Classical Logic can be faithfully encoded. Our calculus enjoys confluence without…
In computer science, various logical languages are defined to analyze properties of systems. One way to pinpoint the essential differences between those logics is to compare their expressivity in terms of distinguishing power and expressive…
Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.
Dummett's logic LC is intuitionistic logic extended with Dummett's axiom: for every two statements the first implies the second or the second implies the first. We present a natural deduction and a Curry-Howard correspondence for…
Inquisitive team logic is a variant of inquisitive logic interpreted in team semantics, which has been argued to provide a natural setting for the regimentation of dependence claims. With respect to sentences, this logic is known to be…