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Working in a semi-constructive logical system that supports the extraction of concurrent programs, we extract a program inverting non-singular real valued matrices from a constructive proof based on Gaussian elimination. Concurrency is used…
We consider an extension of bi-intuitionistic logic with the traditional modalities from tense logic Kt. Proof theoretically, this extension is obtained simply by extending an existing sequent calculus for bi-intuitionistic logic with…
A recent result in [2] on the non-existence of Gauss-Lobatto cubature rules on the triangle is strengthened by establishing a lower bound for the number of nodes of such rules. A method of constructing Lobatto type cubature rules on the…
It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an…
Bi-intuitionistic logic is the extension of intuitionistic logic with a connective dual to implication. Bi-intuitionistic logic was introduced by Rauszer as a Hilbert calculus with algebraic and Kripke semantics. But her subsequent…
We study contact resolutions of Jacobi structures which are contact on an open subset. We give several classes of examples, as well as classes for which it cannot exist.
We present a novel approach to answering sequential questions based on structured objects such as knowledge bases or tables without using a logical form as an intermediate representation. We encode tables as graphs using a graph neural…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
A core component of a successful artificial general intelligence would be the rapid creation and manipulation of grounded compositional abstractions and the demonstration of expertise in the family of recursive hierarchical syntactic…
Using an algebraic orbifold method, we present non-commutative aspects of $G_2$ structure of seven dimensional real manifolds. We first develop and solve the non commutativity parameter constraint equations defining $G_2$ manifold algebras.…
The logic of bunched implications (BI) is a substructural logic that forms the backbone of separation logic, the much studied logic for reasoning about heap-manipulating programs. Although the proof theory and metatheory of BI are…
Input/Output (I/O) logic is a general framework for reasoning about conditional norms and/or causal relations. We streamline Bochman's causal I/O logics via proof-search-oriented sequent calculi. Our calculi establish a natural syntactic…
We describe a new, generally applicable strategy for the systematic construction of basis invariants (BIs). Our method allows one to count the number of mutually independent BIs and gives controlled access to the interrelations (syzygies)…
The formalization of process algebras usually starts with a minimal core of operators and rules for its transition system, and then relax the system to improve its usability and ease the proofs. In the calculus of communicating systems…
In all structural models, the section or fiber response is a relation between the strain measures and the stress resultants. This relation can only be expressed in a simple analytical form when the material response is linear elastic. For…
A novel development is given of the theory of Gaussian quadrature, not relying on the theory of orthogonal polynomials. A method is given for computing the nodes and weights that is manifestly independent of choice of basis in the space of…
Linear structural equation models are multivariate statistical models encoded by mixed graphs. In particular, the set of covariance matrices for distributions belonging to a linear structural equation model for a fixed mixed graph $G=(V,…
Constructor rewriting systems are said to be cons-free if any constructor term occurring in the rhs of a rule must be a subterm of the lhs of the rule. Roughly, such systems cannot build new data structures during their evaluation. In…
We present an intuitionistic interpretation of Euler-Venn diagrams with respect to Heyting algebras. In contrast to classical Euler-Venn diagrams, we treat shaded and missing zones differently, to have diagrammatic representations of…
The causal structure of a unitary transformation is the set of relations of possible influence between any input subsystem and any output subsystem. We study whether such causal structure can be understood in terms of compositional…