Related papers: Some Closed Classes of Three-Valued Logic Generate…
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…
We explore the structure of $\text{Fil}$, the category of filters and germs of admissible partial functions. In particular, we show that $\text{Fil}$ is a nonsymmetric closed category, as defined elsewhere by this and other authors.
With the couplings between the eight gluons constrained by the structure constants of the su(3) algebra in QCD, one would expect that there should exist a special basis (or set of bases) for the algebra wherein, unlike in a Cartan-Weyl…
In this paper we introduce a new class of tuple-generating dependencies (TGDs) called triangularly-guarded (TG) TGDs. We show that conjunctive query answering under this new class of TGDs is decidable since this new class of TGDs also…
We define Boolean algebras in the linear context and study its symmetric powers. We give explicit formulae for products in symmetric Boolean algebras of various dimensions. We formulate symmetric forms of the inclusion-exclusion principle.
In this paper we introduce a new class of tuple-generating dependencies (TGDs) called triangularly-guarded TGDs, which are TGDs with certain restrictions on the atomic derivation track embedded in the underlying rule set. We show that…
We construct bases of quasi-symmetric functions whose product rule is given by the shuffle of binary words, as for multiple zeta values in their integral representations, and then extend the construction to the algebra of free…
We present a uniform characterisation of three-valued logics by means of the bisequent calculus (BSC). It is a generalised form of a sequent calculus (SC) where rules operate on the ordered pairs of ordinary sequents. BSC may be treated as…
We study the class of Lorentzian symmetric polynomials and Lorentzian symmetric functions, which are defined to be symmetric functions for which every truncation of variables is Lorentzian. Similar to the space of Lorentzian polynomials, we…
We study many-valued coalgebraic logics with semi-primal algebras of truth-degrees. We provide a systematic way to lift endofunctors defined on the variety of Boolean algebras to endofunctors on the variety generated by a semi-primal…
Some fixed point results are given for a class of functional contractions acting on (reflexive) triangular symmetric spaces. Technical connections with the corresponding theories over (standard) metric and partial metric spaces are also…
We give a construction of triangulated categories as quotients of exact categories where the subclass of objects sent to zero is defined by a triple of functors. This includes the cases of homotopy and stable module categories. These…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
We show that three fixed point structures equipped with (sequential) composition, a sum operation, and a fixed point operation share the same valid equations. These are the theories of (context-free) languages, (regular) tree languages, and…
The Three Gap Theorem states that for any $\alpha \in \mathbb{R}$ and $N \in \mathbb{N}$, the fractional parts of $\{ 0\alpha, 1\alpha, \dots, (N - 1)\alpha \}$ partition the unit circle into gaps of at most three distinct lengths. We prove…
The paper is dedicated to the problem of adding a modality to the \Lukasiewicz many-valued logics in the purpose of obtaining completeness results for Kripke semantics. We define a class of modal many-valued logics and their corresponding…
The space of constructible functions form a dense subspace of the space of generalized valuations. In this note we prove a somewhat stronger property that the sequential closure, taken sufficiently many (in fact, infinitely many) times, of…
The logic of nulls in databases has been subject of investigation since their introduction in Codd's Relational Model, which is the foundation of the SQL standard. We show a logical characterisation of a first-order fragment of SQL with…
The present work presents some results about the categorial relation between logics and its categories of structures. A (propositional, finitary) logic is a pair given by a signature and Tarskian consequence relation on its formula algebra.…
The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this…