393 research outputs found
A Survey of Languages for Specifying Dynamics: A Knowledge Engineering Perspective
A number of formal specification languages for knowledge-based systems has been developed. Characteristics for knowledge-based systems are a complex knowledge base and an inference engine which uses this knowledge to solve a given problem. Specification languages for knowledge-based systems have to cover both aspects. They have to provide the means to specify a complex and large amount of knowledge and they have to provide the means to specify the dynamic reasoning behavior of a knowledge-based system. We focus on the second aspect. For this purpose, we survey existing approaches for specifying dynamic behavior in related areas of research. In fact, we have taken approaches for the specification of information systems (Language for Conceptual Modeling and TROLL), approaches for the specification of database updates and logic programming (Transaction Logic and Dynamic Database Logic) and the generic specification framework of abstract state machine
Dualized Simple Type Theory
We propose a new bi-intuitionistic type theory called Dualized Type Theory
(DTT). It is a simple type theory with perfect intuitionistic duality, and
corresponds to a single-sided polarized sequent calculus. We prove DTT strongly
normalizing, and prove type preservation. DTT is based on a new propositional
bi-intuitionistic logic called Dualized Intuitionistic Logic (DIL) that builds
on Pinto and Uustalu's logic L. DIL is a simplification of L by removing
several admissible inference rules while maintaining consistency and
completeness. Furthermore, DIL is defined using a dualized syntax by labeling
formulas and logical connectives with polarities thus reducing the number of
inference rules needed to define the logic. We give a direct proof of
consistency, but prove completeness by reduction to L.Comment: 47 pages, 10 figure
Towards an Intelligent Tutor for Mathematical Proofs
Computer-supported learning is an increasingly important form of study since
it allows for independent learning and individualized instruction. In this
paper, we discuss a novel approach to developing an intelligent tutoring system
for teaching textbook-style mathematical proofs. We characterize the
particularities of the domain and discuss common ITS design models. Our
approach is motivated by phenomena found in a corpus of tutorial dialogs that
were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor
for textbook-style mathematical proofs can be built on top of an adapted
assertion-level proof assistant by reusing representations and proof search
strategies originally developed for automated and interactive theorem proving.
The resulting prototype was successfully evaluated on a corpus of tutorial
dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453
The intuitionistic fragment of computability logic at the propositional level
This paper presents a soundness and completeness proof for propositional
intuitionistic calculus with respect to the semantics of computability logic.
The latter interprets formulas as interactive computational problems,
formalized as games between a machine and its environment. Intuitionistic
implication is understood as algorithmic reduction in the weakest possible --
and hence most natural -- sense, disjunction and conjunction as
deterministic-choice combinations of problems (disjunction = machine's choice,
conjunction = environment's choice), and "absurd" as a computational problem of
universal strength. See http://www.cis.upenn.edu/~giorgi/cl.html for a
comprehensive online source on computability logic
Comparing Infinitary Systems for Linear Logic with Fixed Points
Extensions of Girard's linear logic by least and greatest fixed point operators (”MALL) have been an active field of research for almost two decades. Various proof systems are known viz. finitary and non-wellfounded, based on explicit and implicit (co)induction respectively. In this paper, we compare the relative expressivity, at the level of provability, of two complementary infinitary proof systems: finitely branching non-wellfounded proofs (”MALL8) vs. infinitely branching well-founded proofs (”MALL?,8). Our main result is that ”MALL8 is strictly contained in ”MALL?,8. For inclusion, we devise a novel technique involving infinitary rewriting of non-wellfounded proofs that yields a wellfounded proof in the limit. For strictness of the inclusion, we improve previously known lower bounds on ”MALL8 provability from ?01 -hard to S11 -hard, by encoding a sort of BĂŒchi condition for Minsky machines.</p
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