Related papers: Linear Logic for Meaning Assembly
Large language models (LLMs) are increasingly used in situations where human values are at stake, such as decision-making tasks that involve reasoning when performed by humans. We investigate the so-called reasoning capabilities of LLMs…
Semantic parsing is the task of producing a structured meaning representation for natural language utterances or questions. Recent research has pointed out that the commonly-used sequence-to-sequence (seq2seq) semantic parsers struggle to…
The unique capabilities of Large Language Models (LLMs), such as the natural language text generation ability, position them as strong candidates for providing explanation for recommendations. However, despite the size of the LLM, most…
We introduce a logic, called LT, to express properties of transductions, i.e. binary relations from input to output (finite) words. In LT, the input/output dependencies are modelled via an origin function which associates to any position of…
Proofs, in Ludics, have an interpretation provided by their counter-proofs, that is the objects they interact with. We follow the same idea by proposing that sentence meanings are given by the counter-meanings they are opposed to in a…
Logic can be made useful for programming and for databases independently of logic programming. To be useful in this way, logic has to provide a mechanism for the definition of new functions and new relations on the basis of those given in…
Time is deeply woven into how people perceive, and communicate about the world. Almost unconsciously, we provide our language utterances with temporal cues, like verb tenses, and we can hardly produce sentences without such cues. Extracting…
Assurance arguments provide a clear and structured way to explain why stakeholders should trust that a system satisfies certain properties, yet widely used notations, e.g.Goal Structuring Notation (GSN), typically lack an operational…
Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…
Logical reasoning of text requires understanding critical logical information in the text and performing inference over them. Large-scale pre-trained models for logical reasoning mainly focus on word-level semantics of text while struggling…
The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of…
Log-linear models provide a statistically sound framework for Stochastic ``Unification-Based'' Grammars (SUBGs) and stochastic versions of other kinds of grammars. We describe two computationally-tractable ways of estimating the parameters…
Rule-based reasoning over natural language input arises in domains where decisions must be auditable and justifiable: clinical protocols specify eligibility criteria in prose, evidence rules define admissibility through textual conditions,…
Although Large Language Models (LLMs) have demonstrated impressive formal reasoning abilities, they often break down when problems require complex proof planning. One promising approach for improving LLM reasoning abilities involves…
In this paper we present a fully lexicalized grammar formalism as a particularly attractive framework for the specification of natural language grammars. We discuss in detail Feature-based, Lexicalized Tree Adjoining Grammars (FB-LTAGs), a…
Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has…
Analogical reasoning -- the capacity to identify and map structural relationships between different domains -- is fundamental to human cognition and learning. Recent studies have shown that large language models (LLMs) can sometimes match…
This paper addresses the problem of mapping natural language sentences to lambda-calculus encodings of their meaning. We describe a learning algorithm that takes as input a training set of sentences labeled with expressions in the lambda…
We propose FC, a new logic on words that combines finite model theory with the theory of concatenation - a first-order logic that is based on word equations. Like the theory of concatenation, FC is built around word equations; in contrast…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…