68,532 research outputs found
A Meta-Logic of Inference Rules: Syntax
This work was intended to be an attempt to introduce the meta-language for
working with multiple-conclusion inference rules that admit asserted
propositions along with the rejected propositions. The presence of rejected
propositions, and especially the presence of the rule of reverse substitution,
requires certain change the definition of structurality
Structural completeness in propositional logics of dependence
In this paper we prove that three of the main propositional logics of
dependence (including propositional dependence logic and inquisitive logic),
none of which is structural, are structurally complete with respect to a class
of substitutions under which the logics are closed. We obtain an analogues
result with respect to stable substitutions, for the negative variants of some
well-known intermediate logics, which are intermediate theories that are
closely related to inquisitive logic
Identities in the Algebra of Partial Maps
We consider the identities of a variety of semigroup-related algebras modelling the algebra of partial maps. We show that the identities are intimately related to a weak semigroup deductive system and we show that the equational theory is decidable. We do this by giving a term rewriting system for the variety. We then show that this variety has many subvarieties whose equational theory interprets the full uniform word problem for semigroups and consequently are undecidable. As a corollary it is shown that the equational theory of Clifford semigroups whose natural order is a semilattice is undecidable
Reflective Argumentation
Theories of argumentation usually focus on arguments as means of persuasion, finding consensus, or justifying knowledge claims. However, the construction and visualization of arguments can also be used to clarify one's own thinking and to stimulate change of this thinking if gaps, unjustified assumptions, contradictions, or open questions can be identified. This is what I call "reflective argumentation." The objective of this paper is, first, to clarify the conditions of reflective argumentation and, second, to discuss the possibilities of argument visualization methods in supporting reflection and cognitive change. After a discussion of the cognitive problems we are facing in conflicts--obviously the area where cognitive change is hardest--the second part will, based on this, determine a set of requirements argument visualization tools should fulfill if their main purpose is stimulating reflection and cognitive change. In the third part, I will evaluate available argument visualization methods with regard to these requirements and talk about their limitations. The fourth part, then, introduces a new method of argument visualization which I call Logical Argument Mapping (LAM). LAM has specifically been designed to support reflective argumentation. Since it uses primarily deductively valid argument schemes, this design decision has to be justified with regard to goals of reflective argumentation. The fifth part, finally, provides an example of how Logical Argument Mapping could be used as a method of reflective argumentation in a political controversy
A Rule-Based Approach to Analyzing Database Schema Objects with Datalog
Database schema elements such as tables, views, triggers and functions are
typically defined with many interrelationships. In order to support database
users in understanding a given schema, a rule-based approach for analyzing the
respective dependencies is proposed using Datalog expressions. We show that
many interesting properties of schema elements can be systematically determined
this way. The expressiveness of the proposed analysis is exemplarily shown with
the problem of computing induced functional dependencies for derived relations.
The propagation of functional dependencies plays an important role in data
integration and query optimization but represents an undecidable problem in
general. And yet, our rule-based analysis covers all relational operators as
well as linear recursive expressions in a systematic way showing the depth of
analysis possible by our proposal. The analysis of functional dependencies is
well-integrated in a uniform approach to analyzing dependencies between schema
elements in general.Comment: Pre-proceedings paper presented at the 27th International Symposium
on Logic-Based Program Synthesis and Transformation (LOPSTR 2017), Namur,
Belgium, 10-12 October 2017 (arXiv:1708.07854
- …