相关论文: Predicate Transformers, (co)Monads and Resolutions

Two very basic constructions involving experimental procedures are the formation of coarse-grained versions of experiments, and the formation of branching sequential experiments. The latter allow for the conditioning of states on the…

The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…

In the present paper we consider modal propositional logic and look for the constraints that are imposed to the propositions of the special type $\Box a$ by the structure of the relevant finite Kripke frame. We translate the usual language…

We present a logically principled foundation for systematizing, in a way that works with any computational effect and evaluation order, SMT constraint generation seen in refinement type systems for functional programming languages. By…

The study deals with the theory of interior capacities of condensers in a locally compact space, a condenser being treated here as a countable, locally finite collection of arbitrary sets with the sign +1 or -1 prescribed such that the…

Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal,…

The correlators of two-dimensional rational conformal field theories that are obtained in the TFT construction of [FRSI,FRSII,FRSIV] are shown to be invariant under the action of the relative modular group and to obey bulk and boundary…

For a positive real $\alpha$, we can consider the additive submonoid $M$ of the real line that is generated by the nonnegative powers of $\alpha$. When $\alpha$ is transcendental, $M$ is a unique factorization monoid. However, when $\alpha$…

We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighted pluripotential theoretic framework. Indeed, in the…

We examine the problem of projecting subsets of a commutative, positively ordered monoid into an $o$-ideal. We prove that to this end one may restrict to a sufficient subset, for whose cardinality we provide an explicit upper bound. Several…

One way of interpreting a left Kan extension is as taking a kind of "partial colimit", whereby one replaces parts of a diagram by their colimits. We make this intuition precise by means of the "partial evaluations" sitting in the so-called…

Recent research has established complexity results for the problem of deciding the existence of interpolants in logics lacking the Craig Interpolation Property (CIP). The proof techniques developed so far are non-constructive, and no…

We give necessary and sufficient conditions for majorization of realrooted polynomials sharing a common interlacer by means of residues coming from fraction decomposition. We also introduce a motivated notion called strong majorization, and…

We give a new proof of a theorem of Mints that the positive fragment of minimal predicate logic is decidable. The idea of the proof is to replace the eigenvariable condition of sequent calculus by an appropriate scoping mechanism. The…

Several studies have reported the inability of Transformer models to generalize compositionally, a key type of generalization in many NLP tasks such as semantic parsing. In this paper we explore the design space of Transformer models…

A new class of structured matrices is presented and a closed form formula for their determinant is established. This formula has strong connections with the one for Vandermonde matrices.

In this paper, we obtain some factorization results on formal power series over principle ideal domains with sharp bounds on number of irreducible factors. These factorization results correspondingly lead to irreducibility criteria for…

Predicate logic is the premier choice for specifying classes of relational structures. Homomorphisms are key to describing correspondences between relational structures. Questions concerning the interdependencies between these two means of…

State monads in cartesian closed categories are those defined by the familiar adjunction between product and exponential. We investigate the structure of their algebras, and show that the exponential functor is monadic provided the base…

We study the existence and left properness of transferred model structures for "monoid-like" objects in monoidal model categories. These include genuine monoids, but also all kinds of operads as for instance symmetric, cyclic, modular,…