Related papers: Description Logics Go Second-Order -- Extending EL…
Uniform one-dimensional fragment UF1^= is a formalism obtained from first-order logic by limiting quantification to applications of blocks of existential (universal) quantifiers such that at most one variable remains free in the quantified…
Spatial conjunction is a powerful construct for reasoning about dynamically allocated data structures, as well as concurrent, distributed and mobile computation. While researchers have identified many uses of spatial conjunction, its…
Standpoint extensions of knowledge representation formalisms have been recently introduced as a means to incorporate multi-perspective modelling and reasoning through modal operators that attribute pieces of knowledge to specific entities…
The semantics of determiner phrases, be they definite de- scriptions, indefinite descriptions or quantified noun phrases, is often as- sumed to be a fully solved question: common nouns are properties, and determiners are generalised…
This article introduces a relatively complete proof calculus for differential dynamic logic (dL) that is entirely based on uniform substitution, a proof rule that substitutes a formula for a predicate symbol everywhere. Uniform…
In Formal Concept Analysis, a base for a finite structure is a set of implications that characterizes all valid implications of the structure. This notion can be adapted to the context of Description Logic, where the base consists of a set…
In this note we contribute to the recently developing study of "almost Boolean" quantum logics (i.e. to the study of orthomodular partially ordered sets that are naturally endowed with a symmetric difference). We call them enriched quantum…
We define the notion of a model of higher-order modal logic in an arbitrary elementary topos $\mathcal{E}$. In contrast to the well-known interpretation of (non-modal) higher-order logic, the type of propositions is not interpreted by the…
Circumscription is one of the main approaches for defining non-monotonic description logics (DLs). While the decidability and complexity of traditional reasoning tasks such as satisfiability of circumscribed DL knowledge bases (KBs) is well…
Disentangling the explanatory factors in complex data is a promising approach for generalizable and data-efficient representation learning. While a variety of quantitative metrics for learning and evaluating disentangled representations…
Semantic parsing is the task of obtaining machine-interpretable representations from natural language text. We consider one such formal representation - First-Order Logic (FOL) and explore the capability of neural models in parsing English…
This paper concerns an expansion of first-order Belnap-Dunn logic whose connectives and quantifiers all have a counterpart in classical logic. The language and logical consequence relation of this paradefinite logic are defined, a sequent…
Logically constrained term rewriting is a rewriting framework that supports built-in data structures such as integers and bit vectors. Recently, constrained terms play a key role in various analyses and applications of logically constrained…
A growing interest in tasks involving language understanding by the NLP community has led to the need for effective semantic parsing and inference. Modern NLP systems use semantic representations that do not quite fulfill the nuanced needs…
We present a non-deterministic semantic framework for all modal logics in the modal cube, extending prior works by Kearns and others. Our approach introduces modular and uniform multi-valued non-deterministic matrices (Nmatrices) for each…
In this paper we present an alternative approach to formalize the theory of logic programming. In this formalization we allow existential quantified variables and equations in queries. In opposite to standard approaches the role of answer…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
Semiring semantics for first-order logic provides a way to trace how facts represented by a model are used to deduce satisfaction of a formula. Team semantics is a framework for studying logics of dependence and independence in diverse…
Existential rules are an expressive knowledge representation language mainly developed to query data. In the literature, they are often supposed to be in some normal form that simplifies technical developments. For instance, a common…
Quantified Boolean logic results from adding operators to Boolean logic for existentially and universally quantifying variables. This extends the reach of Boolean logic by enabling a variety of applications that have been explored over the…