Related papers: Gradual Classical Logic for Attributed Objects
Proofs, in Ludics, have an interpretation provided by their counter-proofs, that is the objects they interact with. We follow the same idea by proposing that sentence meanings are given by the counter-meanings they are opposed to in a…
Functional relationships between objects, called `attributes', are of considerable importance in knowledge representation languages, including Description Logics (DLs). A study of the literature indicates that papers have made, often…
Can artificial intelligence discover, from raw experience and without human supervision, concepts that humans have discovered? One challenge is that human concepts themselves are fluid: conceptual boundaries can shift, split, and merge as…
Learning commonsense knowledge from natural language text is nontrivial due to reporting bias: people rarely state the obvious, e.g., "My house is bigger than me." However, while rarely stated explicitly, this trivial everyday knowledge…
Humans have a rich representation of the entities in their environment. Entities are described by their attributes, and entities that share attributes are often semantically related. For example, if two books have "Natural Language…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
Attributes of words and relations between two words are central to numerous tasks in Artificial Intelligence such as knowledge representation, similarity measurement, and analogy detection. Often when two words share one or more attributes…
Interactive theorem provers based on dependent type theory have the flexibility to support both constructive and classical reasoning. Constructive reasoning is supported natively by dependent type theory and classical reasoning is typically…
For a newcomer, paraconsistent logics can be difficult to grasp. Even experts in logic can find the concept of paraconsistency to be suspicious or misguided, if not actually wrong. The problem is that although they usually have much in…
Computability logic is a formal theory of (interactive) computability in the same sense as classical logic is a formal theory of truth. This approach was initiated very recently in "Introduction to computability logic" (Annals of Pure and…
We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…
Good quality explanations strengthen the understanding of language models and data. Feature attribution methods, such as Integrated Gradient, are a type of post-hoc explainer that can provide token-level insights. However, explanations on…
Previously, gradual verification has been developed using overapproximating logics such as Hoare logic. We show that the static verification component of gradual verification is also connected to underapproximating logics like incorrectness…
We observe some puzzling linguistic data concerning ordinary knowledge ascriptions that embed an epistemic (im)possibility claim. We conclude that it is untenable to jointly endorse both classical logic and a pair of intuitively attractive…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
Intuitionistic logic extended with decidable propositional atoms combines classical properties in its propositional part and intuitionistic properties for derivable formulas not containing propositional symbols. Sequent calculus is used as…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
The primary theme of this investigation is a decision theoretic account of conditional ought statements (e.g., "You ought to do A, if C") that rectifies glaring deficiencies in classical deontic logic. The resulting account forms a sound…
In this paper we make a contribution to the unification of formal models of defeasible reasoning. We present several translations between formal argumentation frameworks and nonmonotonic logics for reasoning with plausible assumptions. More…
Many semantical aspects of programming languages, such as their operational semantics and their type assignment calculi, are specified by describing appropriate proof systems. Recent research has identified two proof-theoretic features that…