# Extensions to Justification Theory

@article{Marynissen2019ExtensionsTJ, title={Extensions to Justification Theory}, author={Simon Marynissen}, journal={ArXiv}, year={2019}, volume={abs/1905.06184} }

Justification theory is a unifying framework for semantics of non-monotonic logics. It is built on the notion of a justification, which intuitively is a graph that explains the truth value of certain facts in a structure. Knowledge representation languages covered by justification theory include logic programs, argumentation frameworks, inductive definitions, and nested inductive and coinductive definitions. In addition, justifications are also used for implementation purposes. They are used to…

## References

SHOWING 1-10 OF 13 REFERENCES

### Consistency in Justification Theory ∗

- Philosophy, Computer Science
- 2018

A notion of splittable branch evaluation is defined and it is shown that under such an evaluation, justifications can be “glued” together, essentially resulting in a single justification for all true facts.

### A Formal Theory of Justifications

- PhilosophyLPNMR
- 2015

The theory provides elegant and compact formalisations of existing and new semantics in logics of various areas, showing unexpected commonalities and interrelations, and creating opportunities for new expressive knowledge representation formalisms.

### Relevance for SAT(ID)

- Computer ScienceIJCAI
- 2016

A new notion called relevance is presented, which determines a class of literals that are relevant for a given definition and partial interpretation, and shows that choices on irrelevant atoms can never benefit the search for a model.

### Lazy Model Expansion: Interleaving Grounding with Search

- Computer ScienceJ. Artif. Intell. Res.
- 2015

A theoretical framework and an implementation in the context of the FO(ċ) knowledge representation language for Lazily grounding the theory during search, where instead of grounding all parts of a theory, justifications are derived for some parts of it.

### Computing Stable Models of Normal Logic Programs Without Grounding

- Computer ScienceArXiv
- 2017

Using this method, a normal logic program with predicates can be executed directly under the stable model semantics without requiring it to be grounded either before or during execution and without requiring that its variables range over a finite domain.

### Ultimate Well-Founded and Stable Semantics for Logic Programs with Aggregates

- Computer ScienceICLP
- 2001

The approach uses Approximation Theory, a fixpoint theory of stable and well-founded fixpoints of non-monotone operators in a complete lattice to define the syntax of logic programs with aggregates and define the immediate consequence operator of such programs.

### Model Expansion in the Presence of Function Symbols Using Constraint Programming

- Computer Science2013 IEEE 25th International Conference on Tools with Artificial Intelligence
- 2013

An improved approach to handle function symbols in a ground-and-solve methodology, building on ideas from Constraint Programming is presented, in the context of FO(.)IDP, the knowledge representation language that extends First-Order Logic with, among others, inductive definitions, arithmetic and aggregates.

### A Useful Four-Valued Logic

- Philosophy
- 1977

It is argued that a sophisticated question-answering machine that has the capability of making inferences from its data base should employ a certain four-valued logic, the motivating consideration…

### Answering the “why” in answer set programming – A survey of explanation approaches

- Computer ScienceTheory and Practice of Logic Programming
- 2019

An overview of approaches that provide an answer to the question of why an answer set is a solution to a given problem, notably off-line justifications, causal graphs, argumentative explanations, and why-not provenance are given, and highlight their similarities and differences.