Related papers: Compositionality of the MSO+U Logic

A condition, in two variants, is given such that if a property P satisfies this condition, then every logic which is at least as strong as first-order logic and can express P fails to have the compactness property. The result is used to…

We survey the logical structure of constructive set theories and point towards directions for future research. Moreover, we analyse the consequences of being extensible for the logical structure of a given constructive set theory. We…

There is a growing need for abstractions in logic specification languages such as FO(.) and ASP. One technique to achieve these abstractions are templates (sometimes called macros). While the semantics of templates are virtually always…

We introduce MTT, a dependent type theory which supports multiple modalities. MTT is parametrized by a mode theory which specifies a collection of modes, modalities, and transformations between them. We show that different choices of mode…

It is a celebrated result of McKinsey and Tarski [28] that S4 is the logic of the closure algebra X+ over any dense-in-itself separable metrizable space. In particular, S4 is the logic of the closure algebra over the reals R, the rationals…

We prove that functionality of compositions of top-down tree transducers is decidable by reducing the problem to the functionality of one top-down tree transducer with look-ahead.

Compositionality proofs in higher-order languages are notoriously involved, and general semantic frameworks guaranteeing compositionality are hard to come by. In particular, Turi and Plotkin's bialgebraic abstract GSOS framework, which has…

This paper describes an alignment-based model for interpreting natural language instructions in context. We approach instruction following as a search over plans, scoring sequences of actions conditioned on structured observations of text…

Both propositional dependence logic and inquisitive logic are expressively complete. As a consequence, every formula with intuitionistic disjunction or intuitionistic implication can be translated equivalently into a formula in the language…

Modal logics have proved useful for many reasoning tasks in symbolic artificial intelligence (AI), such as belief revision, spatial reasoning, among others. On the other hand, mathematical morphology (MM) is a theory for non-linear analysis…

This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…

Dependency syntax represents the structure of a sentence as a tree composed of dependencies, i.e., directed relations between lexical units. While in its more general form any such tree is allowed, in practice many are not plausible or are…

Complex systems of systems (SoS) are characterized by multiple interconnected subsystems. Typically, each subsystem is designed and analyzed using methodologies and formalisms that are specific to the particular subsystem model of…

Fix an integer h>=1. In the universe of coloured trees of height at most h, we prove that for any graph decision problem defined by an MSO formula with r quantifiers, there exists a set of kernels, each of size bounded by an elementary…

We extend the notion of compositional associative rewriting as recently studied in the rule algebra framework literature to the setting of rewriting rules with conditions. Our methodology is category-theoretical in nature, where the…

Many machine learning algorithms represent input data with vector embeddings or discrete codes. When inputs exhibit compositional structure (e.g. objects built from parts or procedures from subroutines), it is natural to ask whether this…

It is an open question whether compositional truth with the principle of propositional soundness ,,all arithmetical sentences which are propositional tautologies are true'' is conservative over its arithmetical base theory. In this article,…

Dialogue games are two-player logic games between a Proponent who puts forward a logical formula A as valid or true and an Opponent who disputes this. An advantage of the dialogical approach is that it is a uniform framework from which…

We study an abstract notion of tree structure which lies at the common core of various tree-like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested subsets of a set, tree-decompositions of graphs and…

Targeting to use contract-based design for the specification and refinement of extra-functional properties, this research abstract suggests to use type constraints and dependent types to ensure correct and consistent top-down decomposition…