50,333 research outputs found
Using ASP with recent extensions for causal explanations
We examine the practicality for a user of using Answer Set Programming (ASP)
for representing logical formalisms. We choose as an example a formalism aiming
at capturing causal explanations from causal information. We provide an
implementation, showing the naturalness and relative efficiency of this
translation job. We are interested in the ease for writing an ASP program, in
accordance with the claimed ``declarative'' aspect of ASP. Limitations of the
earlier systems (poor data structure and difficulty in reusing pieces of
programs) made that in practice, the ``declarative aspect'' was more
theoretical than practical. We show how recent improvements in working ASP
systems facilitate a lot the translation, even if a few improvements could
still be useful
Space Efficiency of Propositional Knowledge Representation Formalisms
We investigate the space efficiency of a Propositional Knowledge
Representation (PKR) formalism. Intuitively, the space efficiency of a
formalism F in representing a certain piece of knowledge A, is the size of the
shortest formula of F that represents A. In this paper we assume that knowledge
is either a set of propositional interpretations (models) or a set of
propositional formulae (theorems). We provide a formal way of talking about the
relative ability of PKR formalisms to compactly represent a set of models or a
set of theorems. We introduce two new compactness measures, the corresponding
classes, and show that the relative space efficiency of a PKR formalism in
representing models/theorems is directly related to such classes. In
particular, we consider formalisms for nonmonotonic reasoning, such as
circumscription and default logic, as well as belief revision operators and the
stable model semantics for logic programs with negation. One interesting result
is that formalisms with the same time complexity do not necessarily belong to
the same space efficiency class
Takeuti's proof theory in the context of the Kyoto School
Gaisi Takeuti (1926â2017) is one of the most distinguished logicians in proof theory after Hilbert and Gentzen. He extensively extended Hilbert's program in the sense that he formulated Gentzen's sequent calculus, conjectured that cut-elimination holds for it (Takeuti's conjecture), and obtained several stunning results in the 1950â60s towards the solution of his conjecture. Though he has been known chiefly as a great mathematician, he wrote many papers in English and Japanese where he expressed his philosophical thoughts. In particular, he used several keywords such as "active intuition" and "self-reflection" from Nishida's philosophy. In this paper, we aim to describe a general outline of our project to investigate Takeuti's philosophy of mathematics. In particular, after reviewing Takeuti's proof-theoretic results briefly, we describe some key elements in Takeuti's texts. By explaining these texts, we point out the connection between Takeuti's proof theory and Nishida's philosophy and explain the future goals of our project
Hilbert's Program Then and Now
Hilbert's program was an ambitious and wide-ranging project in the philosophy
and foundations of mathematics. In order to "dispose of the foundational
questions in mathematics once and for all, "Hilbert proposed a two-pronged
approach in 1921: first, classical mathematics should be formalized in
axiomatic systems; second, using only restricted, "finitary" means, one should
give proofs of the consistency of these axiomatic systems. Although Godel's
incompleteness theorems show that the program as originally conceived cannot be
carried out, it had many partial successes, and generated important advances in
logical theory and meta-theory, both at the time and since. The article
discusses the historical background and development of Hilbert's program, its
philosophical underpinnings and consequences, and its subsequent development
and influences since the 1930s.Comment: 43 page
New Constructions in Local Quantum Physics
Among several ideas which arose as consequences of modular localization there
are two proposals which promise to be important for the classification and
construction of QFTs. One is based on the observation that wedge-localized
algebras may have particle-like generators with simple properties and the
second one uses the structural simplification of wedge algebras in the
holographic lightfront projection. Factorizable d=1+1 models permit to analyse
the interplay between particle-like aspects and chiral field properties of
lightfront holography. Pacs 11.10.-z, 11.55.-mComment: 21 pages, conference report, references adde
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