Related papers: What do ultraproducts remember about the original …
Ultraproducts are a well-known tool in the classical model theory of first-order logic. We explore their uses in the context of finite model theory.
Paraphrasing methods recognize, generate, or extract phrases, sentences, or longer natural language expressions that convey almost the same information. Textual entailment methods, on the other hand, recognize, generate, or extract pairs of…
Answering a question of Cif\'u Lopes, we give a syntactic characterization of those continuous sentences that are preserved under reduced products of metric structures. In fact, we settle this question in the wider context of general…
We outline basic principles of a new method that gives a conceptual reasoning for and, at the same time, proofs of (super)congruences for truncated sums of arithmetic hypergeometric evaluations.
We use fast-growing finite and infinite sequences of natural numbers and more complicated constructs to define models of hypercomputation and interpret non-arithmetic predicates, with the strongest extensions reaching full second order…
We consider metric ultraproducts of finite groups with respect to some classes of length functions. All sofic groups embed into these ultraproducts. We study embeddings of normed groups. We also show that in some natural situations such an…
We survey various attempts to transport the ultraproduct construction from the realm of model theory to that of general topology.
The functional interpretation is a systematic, syntactic method for transforming certain non-constructive proofs into constructive proofs with explicit bounds. We illustrate the interpretation by working through a concrete, fairly simple…
We present an incomplete proof synthesis method for the Calculus of Constructions which is always terminating and a complete Vernacular for the Calculus of Constructions based on this method.
In the present paper we prove the compactness theorem with respect to partial structures and quasi-truth, using the technique of ultraproducts. Partial structures and quasi-truth are two notions developed within the partial structures…
Copatterns give functional programs a flexible mechanism for responding to their context, and composition can greatly enhance their expressiveness. However, that same expressive power makes it harder to precisely specify the behavior of…
Nested relations, built up from atomic types via product and set types, form a rich data model. Over the last decades the nested relational calculus, NRC, has emerged as a standard language for defining transformations on nested…
In this extended abstract, we propose Structured Production Systems (SPS), which extend traditional production systems with well-formed syntactic structures. Due to the richness of structures, structured production systems significantly…
We generalize the lexicographic product of first-order structures by presenting a framework for constructions which, in a sense, mimic iterating the lexicographic product infinitely and not necessarily countably many times. We then define…
The paper presents two examples of non-traditional using of program specialization by Turchin's supercompilation method. In both cases we are interested in syntactical properties of residual programs produced by supercompilation. In the…
Transformers have been shown to emulate logical deduction over natural language theories (logical rules expressed in natural language), reliably assigning true/false labels to candidate implications. However, their ability to generate…
In a previous publication, we introduced an abstract logic via an abstract notion of quantifier. Drawing upon concepts from categorical logic, this abstract logic interprets formulas from context as subobjects in a specific category, e.g.,…
We present a calculus providing a Curry-Howard correspondence to classical logic represented in the sequent calculus with explicit structural rules, namely weakening and contraction. These structural rules introduce explicit erasure and…
Motivated by the model theory of higher order logics, a certain kind of topological spaces had been introduced on ultraproducts. These spaces are called ultratopologies. Ultratopologies provide a natural extra topological structure for…
Integrating visual and linguistic information into a single multimodal representation is an unsolved problem with wide-reaching applications to both natural language processing and computer vision. In this paper, we present a simple method…