Related papers: A Deductive Account of Quantification in LFG
The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential…
The relationship between communicated language and intended meaning is often probabilistic and sensitive to context. Numerous strategies attempt to estimate such a mapping, often leveraging recursive Bayesian models of communication. In…
We give an introduction to logic tailored for algebraists, explaining how proofs in linear logic can be viewed as algorithms for constructing morphisms in symmetric closed monoidal categories with additional structure. This is made explicit…
This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis of the logical models and…
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…
We investigate compositional structures in data embeddings from pre-trained vision-language models (VLMs). Traditionally, compositionality has been associated with algebraic operations on embeddings of words from a pre-existing vocabulary.…
The AMR (Abstract Meaning Representation) formalism for representing meaning of natural language sentences was not designed to deal with scope and quantifiers. By extending AMR with indices for contexts and formulating constraints on these…
We present a coinductive framework for defining and reasoning about the infinitary analogues of equational logic and term rewriting in a uniform, coinductive way. The setup captures rewrite sequences of arbitrary ordinal length, but it has…
Up to equivalence, a substitution in propositional logic is an endomorphism of its free algebra. On the dual space, this results in a continuous function, and whenever the space carries a natural measure one may ask about the stochastic…
Differentiable logics are a family of quantitative logics originated in the machine learning literature. Because of their origin, differentiable logics often come equipped with analytic properties that guarantee that they are…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
Beginning with a simple semantics for propositions, based on counting observations, it is shown that probabilistic and fuzzy logic correspond to two different heuristic assumptions regarding the combination of propositions whose evidence…
Large Language Models (LLMs) achieve strong performance in analyzing and generating text, yet they struggle with explicit, transparent, and verifiable reasoning over complex texts such as those containing debates. In particular, they lack…
We describe the development of a logic for reasoning about specifications in the Edinburgh Logical Framework (LF). In this logic, typing judgments in LF serve as atomic formulas, and quantification is permitted over contexts and terms that…
This paper introduces LTLF, a temporal logic designed to express the frequency properties of event series in a natural but rigorous manner. By introducing novel, measure-sensitive operators, LTLF allows for the evaluation of frequencies and…
We study the logic obtained by endowing the language of first-order arithmetic with second-order measure quantifiers. This new kind of quantification allows us to express that the argument formula is true in a certain portion of all…
We look at characterizing which formulas are expressible in rich decidable logics such as guarded fixpoint logic, unary negation fixpoint logic, and guarded negation fixpoint logic. We consider semantic characterizations of definability, as…
Multilinear Grammar provides a framework for integrating the many different syntagmatic structures of language into a coherent semiotically based Rank Interpretation Architecture, with default linear grammars at each rank. The architecture…
The dependently-typed lambda calculus LF is often used as a vehicle for formalizing rule-based descriptions of object systems. Proving properties of object systems encoded in this fashion requires reasoning about formulas over LF typing…
Disentangling the explanatory factors in complex data is a promising approach for generalizable and data-efficient representation learning. While a variety of quantitative metrics for learning and evaluating disentangled representations…