Related papers: On Constructive Connectives and Systems
A class of models is presented, in the form of continuation monads polymorphic for first-order individuals, that is sound and complete for minimal intuitionistic predicate logic. The proofs of soundness and completeness are constructive and…
We define a family of propositional constructive modal logics corresponding each to a different classical modal system. The logics are defined in the style of Wijesekera's constructive modal logic, and are both proof-theoretically and…
We propose axioms governing the interaction of constructive assertibility and meaningfulness predicates with a self-applicative truth predicate characterized by the T-scheme, and we prove the consistency of the resulting formal system.
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…
In this paper we consider a general way of constructing profinite struc- tures based on a given framework - a countable family of objects and a countable family of recognisers (e.g. formulas). The main theorem states: A subset of a family…
A structural time series model additively decomposes into generative, semantically-meaningful components, each of which depends on a vector of parameters. We demonstrate that considering each generative component together with its vector of…
We introduce notions of vector field and its (discrete time) flow on a chain complex. The resulting dynamical systems theory provides a set of tools with a broad range of applicability that allow, among others, to replace in a canonical way…
This report introduces and investigates a family of metrics on sets of pointed Kripke models. The metrics are generalizations of the Hamming distance applicable to countably infinite binary strings and, by extension, logical theories or…
The categorical compositional distributional model of Coecke, Sadrzadeh and Clark provides a linguistically motivated procedure for computing the meaning of a sentence as a function of the distributional meaning of the words therein. The…
We study the properties of the constructible universe, L, over intuitionistic theories. We give an extended set of fundamental operations which is sufficient to generate the universe over Intuitionistic Kripke-Platek set theory without…
Despite ample evidence that our concepts, our cognitive architecture, and mathematics itself are all deeply compositional, few models take advantage of this structure. We therefore propose a radically compositional approach to computational…
Conceptual combination performs a fundamental role in creating the broad range of compound phrases utilized in everyday language. This article provides a novel probabilistic framework for assessing whether the semantics of conceptual…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
The equivalence group is determined for systems of linear ordinary differential equations in both the standard form and the normal form. It is then shown that the normal form of linear systems reducible by an invertible point transformation…
We present a unified categorical framework that connects the syntactic Henkin construction for the first-order Completeness Theorem with Lawvere's Fixed-Point Theorem. Concretely, we define two canonical functors from the category 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…
We give a sufficient condition for a model theoretic structure $B$ to 'inherit' quantifier elimination from another structure $A$. This yields an alternative proof of one of the main result from \cite{kle}, namely quantifier elimination for…
We introduce a notion of Kripke model for classical logic for which we constructively prove soundness and cut-free completeness. We discuss the novelty of the notion and its potential applications.
It has been known that there exists a canonical system for every finite real reflection group. The first and the third authors obtained an explicit formula for a canonical system in the previous paper. In this article, we first define…
We study the axiomatisability of the iteration-free fragment of Propositional Dynamic Logic with Intersection and Tests. The combination of program composition, intersection and tests makes its proof-theory rather difficult. We develop a…