Related papers: A Metalanguage for Guarded Iteration
Monoidal computer is a categorical model of intensional computation, where many different programs correspond to the same input-output behavior. The upshot of yet another model of computation is that a categorical formalism should provide a…
Recent studies have highlighted the limitations of large language models in mathematical reasoning, particularly their inability to capture the underlying logic. Inspired by meta-learning, we propose that models should acquire not only…
We propose a learning system in which language is grounded in visual percepts without specific pre-defined categories of terms. We present a unified generative method to acquire a shared semantic/visual embedding that enables the learning…
An important class of decidable first-order logic fragments are those satisfying a guardedness condition, such as the guarded fragment (GF). Usually, decidability for these logics is closely linked to the tree-like model property - the fact…
We present open domain response generation with meta-words. A meta-word is a structured record that describes various attributes of a response, and thus allows us to explicitly model the one-to-many relationship within open domain dialogues…
The logic programming paradigm provides the basis for a new intensional view of higher-order notions. This view is realized primarily by employing the terms of a typed lambda calculus as representational devices and by using a richer form…
Making a linguistic theory is like making a programming language: one typically devises a type system to delineate the acceptable utterances and a denotational semantics to explain observations on their behavior. Via this connection, the…
We present a metagrammatical formalism, {\em generic rules}, to give a default interpretation to grammar rules. Our formalism introduces a process of {\em dynamic binding} interfacing the level of pure grammatical knowledge representation…
Context: Generic programming, as defined by Stepanov, is a methodology for writing efficient and reusable algorithms by considering only the required properties of their underlying data types and operations. Generic programming has proven…
Concatenation hierarchies are classifications of regular languages. All such hierarchies are built through the same construction process: start from an initial class of languages and build new levels using two generic operations.…
We present the first formalization and metatheory of language soundness for a user-schedulable language, the widely used array processing language Halide. User-schedulable languages strike a balance between abstraction and control in…
The trend towards large language models (LLMs) for guardrailing against undesired behaviors is increasing and has shown promise for censoring user inputs. However, increased latency, memory consumption, hosting expenses and non-structured…
Magnitude homology is an invariant of enriched categories which generalizes ordinary categorical homology -- the homology of the classifying space of a small category. The classifying space can also be generalized in a different direction:…
Users of program analyses expect that results change predictably in response to changes in their programs, but many analyses fail to provide such robustness. This paper introduces a theoretical framework that provides a unified language to…
Type soundness is an important property of modern programming languages. In this paper we explore the idea that "well-typed languages are sound": the idea that the appropriate typing discipline over language specifications guarantees that…
An extension to classical unification, called {\em graded unification} is presented. It is capable of combining contradictory information. An interactive processing paradigm and parser based on this new operator are also presented.
We present a categorical framework for formal systems in which inference rules with $m$ metavariables over a category of syntax $\mathscr{S}$, taken to be a cartesian PROP, are represented by operations of arity $k \to n$ equipped with…
Deep learning is currently the subject of intensive study. However, fundamental concepts such as representations are not formally defined -- researchers "know them when they see them" -- and there is no common language for describing and…
This paper introduces MetaDefense, a novel framework for defending against finetuning-based jailbreak attacks in large language models (LLMs). We observe that existing defense mechanisms fail to generalize to harmful queries disguised by…
These notes present a compact and self-contained approach to iterated forcing with a particular emphasis on semiproper forcing. We tried to make our presentation accessible to any scholar who has some familiarity with forcing and boolean…