相关论文: Bijective Faithful Translations among Default Logi…

In the wake of responsible AI, interpretability methods, which attempt to provide an explanation for the predictions of neural models have seen rapid progress. In this work, we are concerned with explanations that are applicable to natural…

Large language models (LLMs) increasingly produce natural language explanations, yet these explanations often lack faithfulness, and they do not reliably reflect the evidence the model uses to decide. We introduce FaithLM, a model-agnostic…

A logic is defined that allows to express information about statistical probabilities and about degrees of belief in specific propositions. By interpreting the two types of probabilities in one common probability space, the semantics given…

Representation theorems for formal systems often take the form of an inductive translation that satisfies certain invariants, which are proved inductively. Theory morphisms and logical relations are common patterns of such inductive…

Bayesian reasoning plays a significant role both in human rationality and in machine learning. In this paper, we introduce transfinite modal logic, which combines modal logic with ordinal arithmetic, in order to formalize Bayesian reasoning…

In this paper, we evaluate the capability of transformer-based language models in making inferences over uncertain text that includes uncertain rules of reasoning. We cover both Pre-trained Language Models (PLMs) and generative Large…

Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…

Argumentation is a non-monotonic process. This reflects the fact that argumentation involves uncertain information, and so new information can cause a change in the conclusions drawn. However, the base logic does not need to be…

Asymmetric combination of logics is a formal process that develops the characteristic features of a specific logic on top of another one. Typical examples include the development of temporal, hybrid, and probabilistic dimensions over a…

The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…

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…

Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…

Logics of limited belief aim at enabling computationally feasible reasoning in highly expressive representation languages. These languages are often dialects of first-order logic with a weaker form of logical entailment that keeps reasoning…

The (extended) AGM postulates for belief revision seem to deal with the revision of a given theory K by an arbitrary formula, but not to constrain the revisions of two different theories by the same formula. A new postulate is proposed and…

The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to…

Qualitative relationships illustrate how changing one property (e.g., moving velocity) affects another (e.g., kinetic energy) and constitutes a considerable portion of textual knowledge. Current approaches use either semantic parsers to…

In default reasoning, usually not all possible ways of resolving conflicts between default rules are acceptable. Criteria expressing acceptable ways of resolving the conflicts may be hardwired in the inference mechanism, for example…

Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts…

In the modern Bayesian view classical probability theory is simply an extension of conventional logic, i.e., a quantitative tool that allows for consistent reasoning in the presence of uncertainty. Classical theory presupposes, however,…

Language models based on the Transformer architecture achieve excellent results in many language-related tasks, such as text classification or sentiment analysis. However, despite the architecture of these models being well-defined, little…