Related papers: Hybrid: A Definitional Two-Level Approach to Reaso…
Logical frameworks and meta-languages form a common substrate for representing, implementing and reasoning about a wide variety of deductive systems of interest in logic and computer science. Their design, implementation and their use in…
Solving symbolic reasoning problems that require compositionality and systematicity is considered one of the key ingredients of human intelligence. However, symbolic reasoning is still a great challenge for deep learning models, which often…
This extended abstract gives a brief outline of the connections between the descriptions and variable concepts. Thus, the notion of a concept is extended to include both the syntax and semantics features. The evaluation map in use is…
Complex reasoning aims to draw a correct inference based on complex rules. As a hallmark of human intelligence, it involves a degree of explicit reading comprehension, interpretation of logical knowledge and complex rule application. In…
Abella is an interactive system for reasoning about aspects of object languages that have been formally presented through recursive rules based on syntactic structure. Abella utilizes a two-level logic approach to specification and…
This paper presents meta-logical investigations based on category theory using the proof assistant Isabelle/HOL. We demonstrate the potential of a free logic based shallow semantic embedding of category theory by providing a formalization…
Reachability Logic is a formalism that can be used, among others, for expressing partial-correctness properties of transition systems. In this paper we present three proof systems for this formalism, all of which are sound and complete and…
Systems for language understanding have become remarkably strong at overcoming linguistic imperfections in tasks involving phrase matching or simple reasoning. Yet, their accuracy drops dramatically as the number of reasoning steps…
Bilingual mathematical problem solving needs a clear link between language reasoning and symbolic calculation. Large language models often handle language well but are weak in accurate computation. This paper presents HERALD (Hybrid…
Classical Decision Theory provides a normative framework for representing and reasoning about complex preferences. Straightforward application of this theory to automate decision making is difficult due to high elicitation cost. In response…
The logic of hereditary Harrop formulas (HH) has proven useful for specifying a wide range of formal systems. This logic includes a form of hypothetical judgment that leads to dynamically changing sets of assumptions and that is key to…
In-context learning (ICL) allows large models to adapt to tasks using a few examples, yet its extension to vision-language models (VLMs) remains fragile. Our analysis reveals that the fundamental limitation lies in an inductive gap, models…
Understanding and manipulating concrete and abstract concepts is fundamental to human intelligence. Yet, they remain challenging for artificial agents. This paper introduces a multimodal generative approach to high order abstract concept…
We propose a coreference annotation scheme as a layer on top of the Universal Conceptual Cognitive Annotation foundational layer, treating units in predicate-argument structure as a basis for entity and event mentions. We argue that this…
Solving complex long-horizon tasks requires strong planning and reasoning capabilities. Although datasets with explicit chain-of-thought (CoT) rationales can substantially benefit learning, they are costly to obtain. To address this…
Conceptual reasoning, the ability to reason in abstract and high-level perspectives, is key to generalization in human cognition. However, limited study has been done on large language models' capability to perform conceptual reasoning. In…
Isabelle/HOL augments classical higher-order logic with ad-hoc overloading of constant definitions---that is, one constant may have several definitions for non-overlapping types. In this paper, we present a mechanised proof that HOL with…
A flexible infrastructure for normative reasoning is outlined. A small-scale demonstrator version of the envisioned system has been implemented in the proof assistant Isabelle/HOL by utilising the first authors universal logical reasoning…
High-level reasoning can be defined as the capability to generalize over knowledge acquired via experience, and to exhibit robust behavior in novel situations. Such form of reasoning is a basic skill in humans, who seamlessly use it in a…
Training large language models (LLMs) with synthetic reasoning data has become a popular approach to enhancing their reasoning capabilities, while a key factor influencing the effectiveness of this paradigm is the quality of the generated…