Related papers: A genuinely untyped solution to the knower paradox…
Algorithms of inference in a computer system oriented to input and semantic processing of text information are presented. Such inference is necessary for logical questions when the direct comparison of objects from a question and database…
We prove that the satisfaction relation $\mathcal{N}\models\varphi[\vec a]$ of first-order logic is not absolute between models of set theory having the structure $\mathcal{N}$ and the formulas $\varphi$ all in common. Two models of set…
Pre-trained models (PTMs) have lead to great improvements in natural language generation (NLG). However, it is still unclear how much commonsense knowledge they possess. With the goal of evaluating commonsense knowledge of NLG models,…
In recent work, Stalnaker proposes a logical framework in which belief is realized as a weakened form of knowledge. Building on Stalnaker's core insights, and using frameworks developed in previous work by Bjorndahl and Baltag et al., we…
Natural language understanding involves reading between the lines with implicit background knowledge. Current systems either rely on pre-trained language models as the sole implicit source of world knowledge, or resort to external knowledge…
We establish completeness for intuitionistic first-order logic, iFOL, showing that a formula is provable if and only if its embedding into minimal logic, mFOL, is uniformly valid under the Brouwer Heyting Kolmogorov (BHK) semantics, the…
Similar to a tree grammar, a Horn theory can be used to describe an infinite set of terms. In this paper, we present a class of Horn theories such that the set of definable predicates is closed wrt. conjunction and such that the…
We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system…
We study the feasibility of identifying epistemic uncertainty (reflecting a lack of knowledge), as opposed to aleatoric uncertainty (reflecting entropy in the underlying distribution), in the outputs of large language models (LLMs) over…
This paper introduces Scavenger, the first theorem prover for pure first-order logic without equality based on the new conflict resolution calculus. Conflict resolution has a restricted resolution inference rule that resembles (a…
The problematic relationship between science and philosophy has, since the beginning of modernity, divided the world into two separate domains: nature and human. Some of today's schools of philosophy and epistemological inquiry have…
We consider a language together with the subword relation, the cover relation, and regular predicates. For such structures, we consider the extension of first-order logic by threshold- and modulo-counting quantifiers. Depending on the…
Standard epistemic logics introduce a modal operator K to represent knowledge, but in doing so they presuppose the logical apparatus they aim to explain. By contrast, this paper explores how logic may be derived from the structure of…
We present a second-order language that can be used to succinctly specify ontologies in a consistent and transparent manner. This language is based on ontology templates (OTTR), a framework for capturing recurring patterns of axioms in…
The prescriptions of our two most prominent strands of decision theory, evidential and causal, differ in a general class of problems known as Newcomb problems. In these, evidential decision theory prescribes choosing a dominated act.…
Knowledge can be represented compactly in a multitude ways, from a set of propositional formulas, to a Kripke model, to a database. In this paper we study the aggregation of information coming from multiple sources, each source submitting a…
Awareness has been shown to be a useful addition to standard epistemic logic for many applications. However, standard propositional logics for knowledge and awareness cannot express the fact that an agent knows that there are facts of which…
Resolving knowledge conflicts is a crucial challenge in Question Answering (QA) tasks, as the internet contains numerous conflicting facts and opinions. While some research has made progress in tackling ambiguous settings where multiple…
The aim of this work is to provide a unified framework for ordinal representations of uncertainty lying at the crosswords between possibility and probability theories. Such confidence relations between events are commonly found in monotonic…
Quantified modal logic provides a natural logical language for reasoning about modal attitudes even while retaining the richness of quantification for referring to predicates over domains. But then most fragments of the logic are…