相关论文: On Defining 'I' "I logy"

The logic of definitions is a family of logics for encoding and reasoning about judgments, which are atomic predicates specified by inference rules. A definition associates an atomic predicate with a logical formula, which may itself depend…

Meaning cannot be based on dictionary definitions all the way down: at some point the circularity of definitions must be broken in some way, by grounding the meanings of certain words in sensorimotor categories learned from experience or…

For more than fifty years, taxonomists have proposed numerous alternative definitions of species while they searched for a unique, comprehensive, and persuasive definition. This monograph shows that these efforts have been unnecessary, and…

We define a relative property A for a countable group with respect to a finite family of subgroups. Many characterizations for relative property A are given. In particular a relative bounded cohomological characterization shows that if a…

We prove two completeness results, one for the extension of dependence logic by a monotone generalized quantifier Q with weak interpretation, weak in the meaning that the interpretation of Q varies with the structures. The second result…

Default logic can be regarded as a mechanism to represent families of belief sets of a reasoning agent. As such, it is inherently second-order. In this paper, we study the problem of representability of a family of theories as the set of…

Many people have proposed definitions of `weak n-category'. Ten of them are presented here. Each definition is given in two pages, with a further two pages on what happens when n = 0, 1, or 2. The definitions can be read independently.…

We give in this paper a logical characterization for unambiguous Context Free Languages, in the vein of descriptive complexity. A fragment of the logic characterizing context free languages given by Lautemann, Schwentick and Th\'erien [18]…

Here, by introducing a version of Unexpected hanging paradox first we try to open a new way and a new explanation for paradoxes, similar to liar paradox. Also, we will show that we have a semantic situation which no syntactical logical…

In [Ben13], the notion of logically distributive category has been introduced to provide a sound and complete semantics to multi-sorted first-order logical theories based on intuitionistic logic. In this note, it will be shown that the…

In this article we present and describe a notion of "logical perfection". We extract the notion of "perfection" from the contemporary logical concept of categoricity. Categoricity (in power) has become in the past half century a main driver…

Given the large variety of existing logical formalisms it is of utmost importance to select the most adequate one for a specific purpose, e.g. for representing the knowledge relevant for a particular application or for using the formalism…

The AI we use is powerful, and its power is increasing rapidly. If this powerful AI is to serve the needs of consumers, voters, and decision makers, then it is imperative that the AI is accountable. In general, an agent is accountable to a…

We say that an ideal I is homogeneous, if its restriction to any I-positive subset is isomorphic to I. The paper investigates basic properties of this notion -- we give examples of homogeneous ideals and present some applications to…

There is a growing frustration amongst researchers and developers in Explainable AI (XAI) around the lack of consensus around what is meant by 'explainability'. Do we need one definition of explainability to rule them all? In this paper, we…

We analyze the informal notion of truth and conclude that it can be formalized in essentially two distinct ways: constructively, in terms of provability, or classically, as a hierarchy of concepts which satisfy Tarski's biconditional in…

Is it possible to articulate a conception of consciousness that is compatible with the exotic characteristics of contemporary, disembodied AI systems, and that can stand up to philosophical scrutiny? How would subjective time and selfhood…

The notions of null-sets and nullity are present in all discourses of mathematics. They are based on the dual-pair of notions of "almost-every" and "almost none". A notion of nullity corresponds to a choice of subsets that one interprets as…

We give an overview of some developments in dependence and independence logic. This is a tiny selection, intended for a newcomer, from a rapidly growing literature on the topic. Furthermore, we discuss conditional independence atoms and we…

We presents an independence relation on sets, one can define dimension by it, assuming that we have an abstract elementary class with a forking notion that satisfies the axioms of a good frame minus stability.