# Theory of Semi-Instantiation in Abstract Argumentation

@article{Gabbay2016TheoryOS,
title={Theory of Semi-Instantiation in Abstract Argumentation},
author={Dov M. Gabbay},
journal={Logica Universalis},
year={2016},
volume={10},
pages={431-516}
}
• D. Gabbay
• Published 27 April 2015
• Computer Science, Philosophy, Mathematics
• Logica Universalis
We study instantiated abstract argumentation frames of the form (S, R, I), where (S, R) is an abstract argumentation frame and where the arguments x of S are instantiated by I(x) as well formed formulas of a well known logic, for example as Boolean formulas or as predicate logic formulas or as modal logic formulas. We use the method of conceptual analysis to derive the properties of our proposed system. We seek to define the notion of complete extensions for such systems and provide algorithms…
6 Citations

### The attack as strong negation, part I

• Computer Science, Philosophy
Log. J. IGPL
• 2015
We add strong negation $N$ to classical logic and interpret the attack relation of "$x$ attacks $y$" in argumentation as $(x\to Ny)$. We write a corresponding object level (using $N$ only) classical

### The attack as intuitionistic negation

• Computer Science
Log. J. IGPL
• 2016
The reduction of argumentation networks to intuitionistic logic yields some additional benefits: it allows us to give semantics to higher level attacks, where an attack can itself attack another attack "$uRv$"; one can make higher level meta-statements $W$ on $(S, R)$ and such meta-Statements can attack and be attacked in the domain.

### Identity Merging and Identity Revision in Talmudic Logic: An Outline Paper

• Philosophy
Computational Models of Rationality
• 2016
This work presents in outline how the Talmud deals with this type of revision, of the form which the authors are calling “identity merging”, where two conflicting bodies of laws apply to the same individual case and they need to decide how to proceed.

### Computing or Estimating Extensions' Probabilities over Structured Probabilistic Argumentation Frameworks

• Computer Science
FLAP
• 2016
The aim is that of experimentally establishing when, due to the complexity of the problem and the size of the structured probabilistic argumentation framework, estimating the extension’s probabilities is preferable to computing it (as computing the probability cannot be done in reasonable time).

### Editorial comment about "On the Difference between ABA and AA"

It is shown that there exist well-studied admissibility-based semantics (semi-stable and eager) under which equivalence does not hold between abstract argumentation and assumption-based argumentation.

## References

SHOWING 1-10 OF 40 REFERENCES

### A Logical Account of Formal Argumentation

• Philosophy
Stud Logica
• 2009
In the current paper, we re-examine how abstract argumentation can be formulated in terms of labellings, and how the resulting theory can be applied in the field of modal logic. In particular, we are

### The attack as strong negation, part I

• Computer Science, Philosophy
Log. J. IGPL
• 2015
We add strong negation $N$ to classical logic and interpret the attack relation of "$x$ attacks $y$" in argumentation as $(x\to Ny)$. We write a corresponding object level (using $N$ only) classical

### A Generalization of Dung's Abstract Framework for Argumentation: Arguing with Sets of Attacking Arguments

• Philosophy, Computer Science
ArgMAS
• 2006
This paper proposes a generalization of the framework of Dung, which allows for sets of arguments to attack other arguments, and proves that all results in the paper by Dung have an equivalent in this more abstract framework.

### Sequent-Based Argumentation for Normative Reasoning

• Computer Science, Philosophy
DEON
• 2014
An argumentative approach to normative reasoning is presented, which adopts a recently proposed framework for logical argumentation in which arguments are generated by a sequent calculus of a given base logic, and uses standard deontic logic as the authors' base logic.

### An abstract framework for argumentation with structured arguments

• H. Prakken
• Philosophy, Computer Science
Argument Comput.
• 2010
An abstract framework for structured arguments is presented, which instantiates Dung's (‘On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming, and

### Foundations of Information and Knowledge Systems

• Philosophy
Lecture Notes in Computer Science
• 2016
We analyze the acceptability dynamics of arguments through the proposal of two different kinds of minimal sets of arguments, core and remainder sets which are somehow responsible for the

### Dialectical Proofs for Constrained Argumentation

• Philosophy
COMMA
• 2010
This work generalizes Dung's frameworks by allowing additional constraints on arguments to be taken into account in the definition of acceptability of arguments, and extends the notion of dialectical proof for D Bung's frameworks in order to respect the additional constraint.

### Dynamic Derivations for Sequent-Based Logical Argumentation

• Computer Science
COMMA
• 2014
This framework accommodates different languages and logics in which arguments may be represented, supports a variety of attack relations, and tolerates dynamic changes in the argumentation setting by revising derivations of assertions in light of new information.