Related papers: Encoding TLA+ set theory into many-sorted first-or…
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…
We develop the theory of partial satisfaction relations for structures that may be proper classes and define a satisfaction predicate appropriate to such structures. We indicate the utility of this theory as a framework for the development…
Transformers, as the fundamental deep learning architecture, have demonstrated great capability in reasoning. This paper studies the generalizable first-order logical reasoning ability of transformers with their parameterized knowledge and…
Continuous representations of logic formulae allow us to integrate symbolic knowledge into data-driven learning algorithms. If such embeddings are semantically consistent, i.e. if similar specifications are mapped into nearby vectors, they…
In this paper we present the first-order logic QLETF+, a quantified version of the logic LETF+, introduced in Coniglio and Rodrigues (Studia Logica 112:561-606, 2024). QLETF+ exhibits several properties that are not always enjoyed by logics…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
A strictly formal, set-theoretical treatment of classical first-order logic is given. Since this is done with the goal of a concrete Mizar formalization of basic results (Lindenbaum lemma; Henkin, satisfiability, completeness and…
We argue that the language of Zermelo Fraenkel set theory with definitions and partial functions provides the most promising bedrock semantics for communicating and sharing mathematical knowledge. We then describe a syntactic sugaring of…
We present automated theorem provers for the first-order logic of here and there (HT). They are based on a native sequent calculus for the logic of HT and an axiomatic embedding of the logic of HT into intuitionistic logic. The analytic…
We introduce DeepPSL a variant of probabilistic soft logic (PSL) to produce an end-to-end trainable system that integrates reasoning and perception. PSL represents first-order logic in terms of a convex graphical model -- hinge-loss Markov…
A semantical embedding of input/output logic in classical higher-order logic is presented. This embedding enables the mechanisation and automation of reasoning tasks in input/output logic with off-the-shelf higher-order theorem provers and…
Large language models (LLMs) have become proficient at solving a wide variety of tasks, including those involving multi-modal inputs. In particular, instantiating an LLM (such as LLaMA) with a speech encoder and training it on paired data…
We introduce a high-level language with Python-like syntax for string-to-string, polyregular, first-order definable transductions. This language features function calls, boolean variables, and nested for-loops. We devise and implement a…
We extend first-order logic to include variadic function symbols, and prove a substitution lemma. Two applications are given: one to bounded quantifier elimination and one to the definability of certain Borel sets.
Human ability at solving complex tasks is helped by priors on object and event semantics of their environment. This paper investigates the use of similar prior knowledge for transfer learning in Reinforcement Learning agents. In particular,…
We continue our investigation into hybrid polyadic multi-sorted logic with a focus on expresivity related to the operational and axiomatic semantics of rogramming languages, and relations with first-order logic. We identify a fragment of…
We present a natural standard translation of inquisitive modal logic InqML into first-order logic over the natural two-sorted relational representations of the intended models, which captures the built-in higher-order features of InqML.…
Separation Logic (SL) with inductive definitions is a natural formalism for specifying complex recursive data structures, used in compositional verification of programs manipulating such structures. The key ingredient of any automated…
We lift the SCL calculus for first-order logic without equality to the SCL(T) calculus for first-order logic without equality modulo a background theory. In a nutshell, the SCL(T) calculus describes a new way to guide hierarchic resolution…
We introduce a powerful approach for Neural Machine Translation (NMT), whereby, during training and testing, together with the input we provide its phonetic encoding and the variants of such an encoding. This way we obtain very significant…