Related papers: Learning Concepts Definable in First-Order Logic w…
A major part of computability theory focuses on the analysis of a few structures of central importance. As a tool, the method of coding with first-order formulas has been applied with great success. For instance, in the c.e. Turing degrees,…
Local-order-invariant (first-order) logic is an extension of first-order logic where formulae have access to a ternary local order relation on the Gaifman graph, provided that the truth value does not depend on the specific order relation…
We consider first-order logic with monoidal quantifiers over words. We show that all languages with a neutral letter, definable using the addition numerical predicate are also definable with the order predicate as the only numerical…
We introduce a restricted second-order logic $\mathrm{SO}^{\mathit{plog}}$ for finite structures where second-order quantification ranges over relations of size at most poly-logarithmic in the size of the structure. We demonstrate the…
A bounded degree structure is either a relational structure all of whose relations are of bounded degree or a functional structure involving bijective functions only. In this paper, we revisit the complexity of the evaluation problem of not…
In a recent article, Alon, Hanneke, Holzman, and Moran (FOCS '21) introduced a unifying framework to study the learnability of classes of partial concepts. One of the central questions studied in their work is whether the learnability of a…
In this paper, we study whether transformer-based language models can extract predicate argument structure from simple sentences. We firstly show that language models sometimes confuse which predicates apply to which objects. To mitigate…
We introduce a quantum analogue of classical first-order logic (FO) and develop a theory of quantum first-order logic as a basis of the productive discussions on the power of logical expressiveness toward quantum computing. The purpose of…
Many known planning tasks have inherent constraints concerning the best order in which to achieve the goals. A number of research efforts have been made to detect such constraints and to use them for guiding search, in the hope of speeding…
Constraint propagation is one of the basic forms of inference in many logic-based reasoning systems. In this paper, we investigate constraint propagation for first-order logic (FO), a suitable language to express a wide variety of…
We show that the decidability of the first-order theory of the language that combines Boolean algebras of sets of uninterpreted elements with Presburger arithmetic operations. We thereby disprove a recent conjecture that this theory is…
Learning classifier systems (LCSs) originated from cognitive-science research but migrated such that LCS became powerful classification techniques. Modern LCSs can be used to extract building blocks of knowledge to solve more difficult…
Various topological concepts are often involved in the research of mathematical logic, and almost all of these concepts can be regarded as developing from the Stone representation theorem. In the Stone representation theorem, a Boolean…
Concept induction requires the extraction and naming of concepts from noisy perceptual experience. For supervised approaches, as the number of concepts grows, so does the number of required training examples. Philosophers, psychologists,…
We study descriptive complexity of counting complexity classes in the range from #P to #$\cdot$NP. A corollary of Fagin's characterization of NP by existential second-order logic is that #P can be logically described as the class of…
We consider the problem of learning generalized first-order representations of concepts from a single example. To address this challenging problem, we augment an inductive logic programming learner with two novel algorithmic contributions.…
We propose a novel learning paradigm for Deep Neural Networks (DNN) by using Boolean logic algebra. We first present the basic differentiable operators of a Boolean system such as conjunction, disjunction and exclusive-OR and show how these…
Transformer architectures have achieved great success in solving natural language tasks, which learn strong language representations from large-scale unlabeled texts. In this paper, we seek to go further beyond and explore a new logical…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
In this article we give several new results on the complexity of algorithms that learn Boolean functions from quantum queries and quantum examples. Hunziker et al. conjectured that for any class C of Boolean functions, the number of quantum…