Related papers: Intentic Semantics for Potentialist Truthmaking
I explore the relationships between Prawitz's approach to non-monotonic proof-theoretic validity, which I call reducibility semantics, and some later proof-theoretic approaches, which I call standard base semantics and Sandqvist's base…
Large Language Models (LLMs) show remarkable capabilities, yet their stochastic next-token prediction creates logical inconsistencies and reward hacking that formal symbolic systems avoid. To bridge this gap, we introduce a formal logic…
Possibilistic logic is a well-known graded logic of uncertainty suitable to reason under incomplete information and partially inconsistent knowledge, which is built upon classical first order logic. There exists for Possibilistic logic a…
Different types of reasoning impose different structural demands on representational systems, yet no systematic account of these demands exists across psychology, AI, and philosophy of mind. I propose a framework identifying four structural…
Justification theory is a general framework for the definition of semantics of rule-based languages that has a high explanatory potential. Nested justification systems, first introduced by Denecker et al. (2015), allow for the composition…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
Recent large-scale neural autoregressive sequence models have shown impressive performances on a variety of natural language generation tasks. However, their generated sequences often exhibit degenerate properties such as non-termination,…
An interpretable system for open-domain reasoning needs to express its reasoning process in a transparent form. Natural language is an attractive representation for this purpose -- it is both highly expressive and easy for humans to…
Recent language models enable new opportunities for structured reasoning with text, such as the construction of intuitive, proof-like textual entailment trees without relying on brittle formal logic. However, progress in this direction has…
At the heart of intuitionistic type theory lies an intuitive semantics called the "meaning explanations"; crucially, when meaning explanations are taken as definitive for type theory, the core notion is no longer "proof" but "verification".…
Formal theories of arithmetic have traditionally been based on either classical or intuitionistic logic, leading to the development of Peano and Heyting arithmetic, respectively. We propose to use $\mu$MALL as a formal theory of arithmetic…
Separation logic is a concise method for specifying programs that manipulate dynamically allocated storage. Partially inspired by separation logic, Implicit Dynamic Frames has recently been proposed, aiming at first-order tool support. In…
We describe a natural deduction formalization of intuitionistic and classical propositional logic in the Isabelle/Pure framework. In contrast to earlier work, where we explored the pedagogical benefits of using a deep embedding approach to…
In many situations humans have to reason with inconsistent knowledge. These inconsistencies may occur due to not fully reliable sources of information. In order to reason with inconsistent knowledge, it is not possible to view a set of…
We recently described a formalism for reasoning with if-then rules that re expressed with different levels of firmness [18]. The formalism interprets these rules as extreme conditional probability statements, specifying orders of magnitude…
Recent work by Chatzi et al. and Ravfogel et al. has developed, for the first time, a method for generating counterfactuals of probabilistic Large Language Models. Such counterfactuals tell us what would - or might - have been the output of…
A central concept within informatics is in modelling such systems for the purpose of reasoning (perhaps automated) about their behaviour and properties. To this end, one requires an interpretation of logical formulae in terms of the…
We present a non-deterministic semantic framework for all modal logics in the modal cube, extending prior works by Kearns and others. Our approach introduces modular and uniform multi-valued non-deterministic matrices (Nmatrices) for each…
Inductive reasoning is a core problem-solving capacity: humans can identify underlying principles from a few examples, which robustly generalize to novel scenarios. Recent work evaluates large language models (LLMs) on inductive reasoning…
We show that explicit pragmatic inference aids in correctly generating and following natural language instructions for complex, sequential tasks. Our pragmatics-enabled models reason about why speakers produce certain instructions, and…