Related papers: An Implemented Formalism for Computing Linguistic …
Two interpretations about syllogistic statements are described in this paper. One is the so-called set-based interpretation, which assumes that quantified statements and syllogisms talk about quantity-relationships between sets. The other…
Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…
We present a simple and concise semantics for temporal planning. Our semantics are developed and formalised in the logic of the interactive theorem prover Isabelle/HOL. We derive from those semantics a validation algorithm for temporal…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
Probabilistic programming provides a convenient lingua franca for writing succinct and rigorous descriptions of probabilistic models and inference tasks. Several probabilistic programming languages, including Anglican, Church or Hakaru,…
We develop a qualitative model of decision making with two aims: to describe how people make simple decisions and to enable computer programs to do the same. Current approaches based on Planning or Decisions Theory either ignore uncertainty…
This paper explores the space of (propositional) probabilistic logical languages, ranging from a purely `qualitative' comparative language to a highly `quantitative' language involving arbitrary polynomials over probability terms. While…
Modal logics allow reasoning about various modes of truth: for example, what it means for something to be possibly true, or to know that something is true as opposed to merely believing it. This report describes embeddings of propositional…
Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive…
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…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…
In this thesis, we present two approaches to a rigorous mathematical and algorithmic foundation of quantitative and statistical inference in constraint-based natural language processing. The first approach, called quantitative constraint…
A grammar formalism based upon CHR is proposed analogously to the way Definite Clause Grammars are defined and implemented on top of Prolog. These grammars execute as robust bottom-up parsers with an inherent treatment of ambiguity and a…
Argumentation is a very active research field of Artificial Intelligence concerned with the representation and evaluation of arguments used in dialogues between humans and/or artificial agents. Acceptability semantics of formal…
We have recently begun a project to develop a more effective and efficient way to marshal inferences from background knowledge to facilitate deep natural language understanding. The meaning of a word is taken to be the entities,…
In this paper we show several similarities among logic systems that deal simultaneously with deductive and quantitative inference. We claim it is appropriate to call the tasks those systems perform as Quantitative Logic Reasoning. Analogous…
We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of…
This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the…
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…