Related papers: First-Order Conditional Logic Revisited
This papers develops a logical language for representing probabilistic causal laws. Our interest in such a language is twofold. First, it can be motivated as a fundamental study of the representation of causal knowledge. Causality has an…
The fuzzy modality `probably` is interpreted over probabilistic type spaces by taking expected truth values. The arising probabilistic fuzzy description logic is invariant under probabilistic bisimilarity; more informatively, it is…
We investigate how the sentence choice semantics (SCS) for propositional superposition logic (PLS) developed in \cite{Tz17} could be extended so as to successfully apply to first-order superposition logic(FOLS). There are two options for…
We consider (finitary, propositional) logics through the original use of Category Theory: the study of the "sociology of mathematical objects", aligning us with a recent, and growing, trend of study logics through its relations with other…
We contribute to the refined understanding of the language-logic-algebra interplay in the context of first-order properties of countable words. We establish decidable algebraic characterizations of one variable fragment of FO as well as…
Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…
Reasoning semantically in first-order logic is notoriously a challenge. This paper surveys a selection of semantically-guided or model-based methods that aim at meeting aspects of this challenge. For first-order logic we touch upon…
Conditionals are useful for modelling, but are not always sufficiently expressive for capturing information accurately. In this paper we make the case for a form of conditional that is situation-based. These conditionals are more expressive…
We develop a characterization of quantum states by means of first order variables and random variables, within a predicative logic with equality, in the framework of basic logic and its definitory equations. We introduce the notion of…
The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of…
We present a method of generating first-order logic statements whose complexity can be controlled along multiple dimensions. We use this method to automatically create several datasets consisting of questions asking for the truth or falsity…
We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization…
With the increasing interest in using large language models (LLMs) for planning in natural language, understanding their behaviors becomes an important research question. This work conducts a systematic investigation of LLMs' ability to…
Bayesian networks provide an elegant formalism for representing and reasoning about uncertainty using probability theory. Theyare a probabilistic extension of propositional logic and, hence, inherit some of the limitations of propositional…
The KLM approach to defeasible reasoning introduces a weakened form of implication into classical logic. This allows one to incorporate exceptions to general rules into a logical system, and for old conclusions to be withdrawn upon learning…
Logical reasoning remains a challenge for natural language processing, but it can be improved by training language models to mimic theorem provers on procedurally generated problems. Previous work used domain-specific proof generation…
We study the reactive synthesis problem for distributed systems with an unbounded number of participants interacting with an uncontrollable environment. Executions of those systems are modeled by data words, and specifications are given as…
We consider an extension of first-order logic with a recursion operator that corresponds to allowing formulas to refer to themselves. We investigate the obtained language under two different systems of semantics, thereby obtaining two…
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…
Plausible reasoning concerns situations whose inherent lack of precision is not quantified; that is, there are no degrees or levels of precision, and hence no use of numbers like probabilities. A hopefully comprehensive set of principles…