Related papers: Big-Stop Semantics: Small-Step Semantics in a Big-…
Synthesizing large logic programs through symbolic Inductive Logic Programming (ILP) typically requires intermediate definitions. However, cluttering the hypothesis space with intensional predicates typically degrades performance. In…
The rules associated with propositional logic programs and the stable model semantics are not expressive enough to let one write concise programs. This problem is alleviated by introducing some new types of propositional rules. Together…
Operational semantics has established itself as a flexible but rigorous means to describe the meaning of programming languages. Oftentimes, it is felt necessary to keep a semantics small, for example to facilitate its use for model checking…
An algorithm for computing the stable model semantics of logic programs is developed. It is shown that one can extend the semantics and the algorithm to handle new and more expressive types of rules. Emphasis is placed on the use of…
Large language models (LLMs) have a substantial capacity for high-level analogical reasoning: reproducing patterns in linear text that occur in their training data (zero-shot evaluation) or in the provided context (few-shot in-context…
Current approaches for training Process Reward Models (PRMs) often involve breaking down responses into multiple reasoning steps using rule-based techniques, such as using predefined placeholder tokens or setting the reasoning step's length…
This paper primarily demonstrates a method to quantitatively assess the alignment between multi-step, structured reasoning in large language models and human preferences. We introduce the Alignment Score, a semantic-level metric that…
Step-indexed semantic interpretations of types were proposed as an alternative to purely syntactic proofs of type safety using subject reduction. The types are interpreted as sets of values indexed by the number of computation steps for…
Large language models are a form of artificial intelligence systems whose primary knowledge consists of the statistical patterns, semantic relationships, and syntactical structures of language1. Despite their limited forms of "knowledge",…
Despite impressive breadth, LLMs still rely on explicit reasoning instructions or static, one-fits-all steering methods, leaving a gap for adaptive, instruction-free reasoning amplification. We present Prototype-Based Dynamic Steering…
I present an analytic approach to establishing the presence of phase transitions in a large set of decision problems. This approach does not require extensive computational study of the problems considered. The set -- that of all paddable…
We investigate the possibility of a semantic account of the execution time (i.e. the number of beta-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value lambda-calculus. For this…
Mathematical reasoning has been challenging for large language models (LLMs), and the introduction of step-by-step Chain-of-Thought (CoT) inference has significantly advanced the mathematical capabilities of LLMs. However, current…
In computational argumentation, gradual semantics are fine-grained alternatives to extension-based and labelling-based semantics . They ascribe a dialectical strength to (components of) arguments sanctioning their degree of acceptability.…
LLMs struggle with Semantic Inertia: the inability to inhibit pre-trained priors (e.g., "Lava is Dangerous") when dynamic, in-context rules contradict them. We probe this phenomenon using Baba Is You, where physical laws are mutable text…
Large language models perform text generation through high-dimensional internal dynamics, yet the temporal organisation of these dynamics remains poorly understood. Most interpretability approaches emphasise static representations or causal…
Many potentially non-terminating functions cannot be directly defined in a logic of total functions, such as HOL. A well-known solution to this is to define non-terminating functions using a clock that forces termination at a certain depth…
Humans have a powerful and mysterious capacity to reason. Working through a set of mental steps enables us to make inferences we would not be capable of making directly even though we get no additional data from the world. Similarly, when…
An approximate program transformation is a transformation that can change the semantics of a program within a specified empirical error bound. Such transformations have wide applications: they can decrease computation time, power…
Large language models show improved downstream task performance when prompted to generate step-by-step reasoning to justify their final answers. These reasoning steps greatly improve model interpretability and verification, but objectively…