Related papers: LP=>: Extending LP with a strong conditional opera…
In this book we promote logical computational linguistics as opposed to statistical computational linguistics. In particular, we provide a logical semantic interface. This book assembles more than twenty years of research work on type…
We introduce the logics GLP(\Lambda), a generalization of Japaridze's polymodal provability logic GLP(\omega) where \Lambda is any linearly ordered set representing a hierarchy of provability operators of increasing strength. We shall…
We will investigate proof-theoretic and linguistic aspects of first-order linear logic. We will show that adding partial order constraints in such a way that each sequent defines a unique linear order on the antecedent formulas of a sequent…
Inferring the abstract relational and causal structure of the world is a major challenge for reinforcement-learning (RL) agents. For humans, language--particularly in the form of explanations--plays a considerable role in overcoming this…
In the theory of answer set programming, two groups of rules are called strongly equivalent if, informally speaking, they have the same meaning in any context. The relationship between strong equivalence and the propositional logic of…
For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to…
A strong version of the Orlicz maximal operator is introduced and a natural $B_p$ condition for the rectangle case is defined to characterize its boundedness. This fact let us to describe a sufficient condition for the two weight…
In this paper, general logic-systems and a necessary and sufficient algorithm are used to substantiate significant consequence operator properties. It is shown, among other results, that, in certain cases, (1) if the number of steps in a…
A logic calculus is presented that is a conservative extension of linear logic. The motivation beneath this work concerns lazy evaluation, true concurrency and interferences in proof search. The calculus includes two new connectives to deal…
We develop first-order logic and some extensions for incomplete information scenarios and consider related complexity issues.
This paper introduces Logical Credal Networks, an expressive probabilistic logic that generalizes many prior models that combine logic and probability. Given imprecise information represented by probability bounds and conditional…
We present a propositional logic %which can be used 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…
The variable inclusion companions of logics have lately been thoroughly studied by multiple authors. There are broadly two types of these companions: the left and the right variable inclusion companions. Another type of companions of logics…
Dynamic logic is a powerful framework for reasoning about imperative programs. An extension with a concurrent operator [18] was introduced to formalise programs running in parallel. In other direction, other authors proposed a systematic…
Description logics (DLs) are well-known knowledge representation formalisms focused on the representation of terminological knowledge. Due to their first-order semantics, these languages (in their classical form) are not suitable for…
As large language models (LLMs) are increasing integrated into fact-checking pipelines, formal logic is often proposed as a rigorous means by which to mitigate bias, errors and hallucinations in these models' outputs. For example, some…
We propose an extension of Strategy Logic (SL), in which one can both reason about strategizing under imperfect information and about players' knowledge. One original aspect of our approach is that we do not force strategies to be uniform,…
Constraint logic grammars provide a powerful formalism for expressing complex logical descriptions of natural language phenomena in exact terms. Describing some of these phenomena may, however, require some form of graded distinctions which…
In this paper, we use a categorical and functorial set up to model the syntax and inference of logics with algebraic signature, extending previous works on algebraisation of logics. The main feature of this work is that structurality, or…
Program logics are a powerful formal method in the context of program verification. Can we develop a counterpart of program logics in the context of language verification? This paper proposes language logics, which allow for statements of…