Related papers: Higher-Order Coloured Unification and Natural Lang…

Systems now exist which are able to compile unification grammars into language models that can be included in a speech recognizer, but it is so far unclear whether non-trivial linguistically principled grammars can be used for this purpose.…

There is an extensive history of scholarship into what constitutes a "basic" color term, as well as a broadly attested acquisition sequence of basic color terms across many languages, as articulated in the seminal work of Berlin and Kay…

In this thesis we use quasiorders on words to offer a new perspective on two well-studied problems from Formal Language Theory: deciding language inclusion and manipulating the finite automata representations of regular languages. First, we…

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…

A novel computational model (CoDD) utilizing combinatory logic to create higher-order decision trees is presented. A theoretical analysis of general intelligence in terms of the formal theory of pattern recognition and pattern formation is…

Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…

Fiore and Hur recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a…

Motivated by applications in automated verification of higher-order functional programs, we develop a notion of constrained Horn clauses in higher-order logic and a decision problem concerning their satisfiability. We show that, although…

The uniform one-dimensional fragment of first-order logic was introduced a few years ago as a generalization of the two-variable fragment of first-order logic to contexts involving relations of arity greater than two. Quantifiers in this…

Two main approaches have been developed for learning first-order planning (action) models from unstructured data: combinatorial approaches that yield crisp action schemas from the structure of the state space, and deep learning approaches…

Automated Theorem Proving (ATP) deals with the development of computer programs being able to show that some conjectures (queries) are a logical consequence of a set of axioms (facts and rules). There exists several successful ATPs where…

Let $\mathcal M=(M,<,...)$ be a linearly ordered first-order structure and $T$ its complete theory. We investigate conditions for $T$ that could guarantee that $\mathcal M$ is not much more complex than some colored orders (linear orders…

Unified multimodal models (UMMs) were designed to combine the reasoning ability of large language models (LLMs) with the generation capability of vision models. In practice, however, this synergy remains elusive: UMMs fail to transfer…

This paper presents a new Unified pre-trained Language Model (UniLM) that can be fine-tuned for both natural language understanding and generation tasks. The model is pre-trained using three types of language modeling tasks: unidirectional,…

The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…

We uncover a close relationship between combinatorial and syntactic proofs for first-order logic (without equality). Whereas syntactic proofs are formalized in a deductive proof system based on inference rules, a combinatorial proof is a…

We show that descriptive complexity's result extends in High Order Logic to capture the expressivity of Turing Machine which have a finite number of alternation and whose time or space is bounded by a finite tower of exponential. Hence we…

This paper proposes a framework combining Neural Ordinary Differential Equations (Neural ODEs) and robust control theory to enhance the interpretability and control of large language models (LLMs). By utilizing Neural ODEs to model the…

The production of color language is essential for grounded language generation. Color descriptions have many challenging properties: they can be vague, compositionally complex, and denotationally rich. We present an effective approach to…

Formal, Distributional, and Grounded theories of computational semantics each have their uses and their drawbacks. There has been a shift to ground models of language by adding visual knowledge, and there has been a call to enrich models of…