相关论文: Turning the Liar paradox into a metatheorem of Bas…

Sub-sub-intuitionistic logic is obtained from intuitionistic logic by weakening the implication and removing distributivity. It can alternatively be viewed as conditional weak positive logic. We provide semantics for sub-sub-intuitionistic…

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…

We introduce a novel logical notion--partial entailment--to propositional logic. In contrast with classical entailment, that a formula P partially entails another formula Q with respect to a background formula set \Gamma intuitively means…

We study the structure of families of theories in the language of arithmetic extended to allow these families to refer to one another and to themselves. If a theory contains schemata expressing its own truth and expressing a specific Turing…

Discourse relations bind smaller linguistic elements into coherent texts. However, automatically identifying discourse relations is difficult, because it requires understanding the semantics of the linked sentences. A more subtle challenge…

We introduce and investigate a family of consequence relations with the goal of capturing certain important patterns of data-driven inference. The inspiring idea for our framework is the fact that data may reject, possibly to some degree,…

This paper is devoted to the investigation of term-definable connexive implications in substructural logics with exchange and, on the semantical perspective, in sub-varieties of commutative residuated lattices (FLe-algebras). In particular,…

We study logical reduction (factorization) of relations into relations of lower arity by Boolean or relative products that come from applying conjunctions and existential quantifiers to predicates, i.e. by primitive positive formulas of…

We give a theoretical model of conjunctions $E\wedge F$ and implications $E\implies F$ where $F$ is meaningful only when $E$ is true, a situation which is very often encountered in everyday mathematics, and which was already formalized by…

We reduce phrase-representation parsing to dependency parsing. Our reduction is grounded on a new intermediate representation, "head-ordered dependency trees", shown to be isomorphic to constituent trees. By encoding order information in…

We extend the framework of abstract algebraic logic to weak logics, namely logical systems which are not necessarily closed under uniform substitution. We interpret weak logics by algebras expanded with an additional predicate and we…

Language models (LMs) trained on large quantities of text have been claimed to acquire abstract linguistic representations. Our work tests the robustness of these abstractions by focusing on the ability of LMs to learn interactions between…

Multiplicative linear logic is a very well studied formal system, and most such studies are concerned with the one-sided sequent calculus. In this paper we look in detail at existing translations between a deep inference system and the…

In this paper, we propose a comprehensive benchmark to investigate models' logical reasoning capabilities in complex real-life scenarios. Current explanation datasets often employ synthetic data with simple reasoning structures. Therefore,…

Recent neural models for relation extraction with distant supervision alleviate the impact of irrelevant sentences in a bag by learning importance weights for the sentences. Efforts thus far have focused on improving extraction accuracy but…

It is standard to regard the intuitionistic restriction of a classical logic as increasing the expressivity of the logic because the classical logic can be adequately represented in the intuitionistic logic by double-negation, while the…

Matching logic is a general formal framework for reasoning about a wide range of theories, with particular emphasis on programming language semantics. Notably, the intermediate language of the K semantics framework is an extension of…

Metonymy and metaphor often co-occur in natural language, yet computational work has studied them largely in isolation. We introduce a framework that transforms a literal sentence into three figurative variants: metonymic, metaphoric, and…

We present a novel approach for teaching logic and the metatheory of logic to students who have some experience with functional programming. We define concepts in logic as a series of functional programs in the language of the proof…

Meta-learning has emerged as an efficient approach for constructing target models based on support sets. For example, the meta-learned embeddings enable the construction of target nearest-neighbor classifiers for specific tasks by pulling…