Related papers: Denotational Correctness of Forward-Mode Automatic…
Algorithmic differentiation (AD) has become increasingly capable and straightforward to use. However, AD is inefficient when applied directly to solvers, a feature of most engineering analyses. We can leverage implicit differentiation to…
Automated reasoning is critical in domains such as law and governance, where verifying claims against facts in documents requires both accuracy and interpretability. Recent work adopts structured reasoning pipelines that translate natural…
We prove that, similarly to known PSpace-completeness of recognising FO(<)-definability of the language L(A) of a DFA A, deciding both FO(<,C)- and FO(<,MOD)-definability are PSpace-complete. (Here, FO(<,C) extends the first-order logic…
We introduce a category-theoreticabstraction of a syntax with auxiliary functions, called an admissiblemonad morphism. Relying on an abstract form of structural recursion,we then design generic tools to construct admissible monad…
Creating a descriptive grammar of a language is an indispensable step for language documentation and preservation. However, at the same time it is a tedious, time-consuming task. In this paper, we take steps towards automating this process…
Dependent type theory gives an expressive type system facilitating succinct formalizations of mathematical concepts. In practice, it is mainly used for interactive theorem proving with intensional type theories, with PVS being a notable…
We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…
In this paper, we introduce the map-language navigation task where an agent executes natural language instructions and moves to the target position based only on a given 3D semantic map. To tackle the task, we design the instruction-aware…
Large Language Models (LLMs) have demonstrated powerful reasoning capabilities through Chain-of-Thought (CoT) in various tasks, yet the inefficiency of token-by-token generation hinders real-world deployment in latency-sensitive recommender…
We present a simple functional programming language, called Dual PCF, that implements forward mode automatic differentiation using dual numbers in the framework of exact real number computation. The main new feature of this language is the…
Several tasks in artificial intelligence require to be able to find models about knowledge dynamics. They include belief revision, fusion and belief merging, and abduction. In this paper we exploit the algebraic framework of mathematical…
Context: Reynolds showed us how to use continuation-passing style and defunctionalization to transform a recursive interpreter for a language into an abstract machine for programs in that language. The same techniques explain other…
Alternating parity automata (APAs) provide a robust formalism for modelling infinite behaviours and play a central role in formal verification. Despite their widespread use, the algebraic theory underlying APAs has remained largely…
Formal semantics provides rigorous, mathematically precise definitions of programming languages, with which we can argue about program behaviour and program equivalence by formal means; in particular, we can describe and verify our…
Among the most general structures extending the framework by Dung are the abstract dialectical frameworks (ADFs). They come equipped with various types of semantics, with the most prominent - the labeling-based one - analyzed in the context…
Diffusion large language models (dLLMs) offer a promising paradigm for parallel text generation, but in practice they face an accuracy-parallelism trade-off, where increasing tokens per forward (TPF) often degrades generation quality.…
Meaning Representation (AMR) is a semantic representation for natural language that embeds annotations related to traditional tasks such as named entity recognition, semantic role labeling, word sense disambiguation and co-reference…
The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual…
We present a small-step, frame stack style, semantics for sequential Core Erlang, a dynamically typed, impure functional programming language. The semantics and the properties that we prove are machine-checked with the Coq proof assistant.…
In this paper we introduce a novel semantics, called defense semantics, for Dung's abstract argumentation frameworks in terms of a notion of (partial) defence, which is a triple encoding that one argument is (partially) defended by another…