Related papers: Some Model Theory of Guarded Negation
Detection and elimination of redundant clauses from propositional formulas in Conjunctive Normal Form (CNF) is a fundamental problem with numerous application domains, including AI, and has been the subject of extensive research. Moreover,…
State-of-the-art deep-learning-based approaches to Natural Language Processing (NLP) are credited with various capabilities that involve reasoning with natural language texts. In this paper we carry out a large-scale empirical study…
In the framework of computable queries in Database Theory, there are many examples of queries to (properties of) relational database instances that can be expressed by simple and elegant third order logic ($\mathrm{TO}$) formulae. In many…
Although self-attention based models such as Transformers have achieved remarkable successes on natural language processing (NLP) tasks, recent studies reveal that they have limitations on modeling sequential transformations (Hahn, 2020),…
How can we enable computers to automatically answer questions like "Who created the character Harry Potter"? Carefully built knowledge bases provide rich sources of facts. However, it remains a challenge to answer factoid questions raised…
Knowledge can be represented compactly in a multitude ways, from a set of propositional formulas, to a Kripke model, to a database. In this paper we study the aggregation of information coming from multiple sources, each source submitting a…
The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory $T$ in which all partially recursive functions are representable, yet $T$…
Blocked clauses provide the basis for powerful reasoning techniques used in SAT, QBF, and DQBF solving. Their definition, which relies on a simple syntactic criterion, guarantees that they are both redundant and easy to find. In this paper,…
Recently, the separated fragment (SF) of first-order logic has been introduced. Its defining principle is that universally and existentially quantified variables may not occur together in atoms. SF properly generalizes both the…
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…
We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…
The categorical compositional distributional model of natural language provides a conceptually motivated procedure to compute the meaning of sentences, given grammatical structure and the meanings of its words. This approach has…
Using a recently introduced algebraic framework for the classification of fragments of first-order logic, we study the complexity of the satisfiability problem for several ordered fragments of first-order logic, which are obtained from the…
Despite the impressive performance of large language models across various tasks, they often struggle with reasoning under negated statements. Negations are important in real-world applications as they encode negative polarity in verb…
Formalisms based on temporal logics interpreted over finite strict linear orders, known in the literature as finite traces, have been used for temporal specification in automated planning, process modelling, (runtime) verification and…
We study Linear Temporal Logic Modulo Theories over Finite Traces (LTLfMT), a recently introduced extension of LTL over finite traces (LTLf) where propositions are replaced by first-order formulas and where first-order variables referring…
Answering Boolean conjunctive queries over the guarded fragment is decidable, however, as yet no practical decision procedure exists. Meanwhile, ordered resolution, as a practically oriented algorithm, is widely used in state-of-art modern…
Despite its simplicity, bag-of-n-grams sen- tence representation has been found to excel in some NLP tasks. However, it has not re- ceived much attention in recent years and fur- ther analysis on its properties is necessary. We propose a…
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…
In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational interpretation of first-order formulas over arbitrary interpretations. Here we complement this work by introducing a denotational semantics for first-order logic.…