# Abductive Reasoning in Intuitionistic Propositional Logic via Theorem Synthesis

@article{Tarau2022AbductiveRI, title={Abductive Reasoning in Intuitionistic Propositional Logic via Theorem Synthesis}, author={Paul Tarau}, journal={Theory and Practice of Logic Programming}, year={2022}, volume={22}, pages={693 - 707} }

Abstract With help of a compact Prolog-based theorem prover for Intuitionistic Propositional Logic, we synthesize minimal assumptions under which a given formula formula becomes a theorem. After applying our synthesis algorithm to cover basic abductive reasoning mechanisms, we synthesize conjunctions of literals that mimic rows of truth tables in classical or intermediate logics and we abduce conditional hypotheses that turn the theorems of classical or intermediate logics into theorems in…

## One Citation

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## References

SHOWING 1-10 OF 14 REFERENCES

### Deriving Theorems in Implicational Linear Logic, Declaratively

- Computer ScienceICLP Technical Communications
- 2020

Combinatorial generation of provable formulas of a given size, intuitionistic and linear logic theorem provers, theorems of the implicational fragment of propositional linear intuitionistic logic, Curry-Howard isomorphism, efficient generation of linear lambda terms in normal form, Prolog programs for lambda term generation and theorem proving.

### Synthesis of Modality Definitions and a Theorem Prover for Epistemic Intuitionistic Logic

- Philosophy, Computer ScienceLOPSTR
- 2020

We propose a mechanism for automating discovery of definitions, that, when added to a logic system for which we have a theorem prover, extends it to support an embedding of a new logic system into…

### A Combinatorial Testing Framework for Intuitionistic Propositional Theorem Provers

- PhilosophyPADL
- 2019

Proving a theorem in intuitionistic propositional logic, with implication as its single connective, is known as one of the simplest to state PSPACE-complete problem. At the same time, via the…

### A New Logical Characterisation of Stable Models and Answer Sets

- Computer ScienceNMELP
- 1996

This paper relates inference in extended logic programming with nonclassical, nonmonotonic logics with equilibrium logic, and shows that on logic programs equilibrium logic coincides with the inference operation associated with the stable model and answer set semantics of Gelfond and Lifschitz.

### A Tableau Calculus for Equilibrium Entailment

- PhilosophyTABLEAUX
- 2000

We apply tableau methods to the problem of computing entailment in the nonmonotonic system of equilibrium logic, a generalisation of the inference relation associated with the stable model and answer…

### Goal Oriented Deductions

- Philosophy
- 2002

This chapter presents a general methodology for automated deduction inspired by the logic programming paradigm and surveys the application of goaldirected methods to classical, intuitionistic, modal, and substructural logics.

### Strongly equivalent logic programs

- Computer ScienceACM Trans. Comput. Log.
- 2001

The main theorem shows that the verification of strong equivalence can be accomplished by cheching the equivalence of formulas in a monotonic logic, called the logic of here-and-there, which is intermediate between classical logic and intuitionistic logic.

### Intuitionistic Decision Procedures Since Gentzen

- Philosophy, Computer Science
- 2016

Solutions to the decision problem for intuitionistic propositional logic are of importance both for general philosophical reasons and because of their use in implementations of proof assistants based on intuitionistic logic.

### Contraction-free sequent calculi for intuitionistic logic

- Computer ScienceJournal of Symbolic Logic
- 1992

An equivalent calculus is described below, yet another variant on these systems, where the problem no longer arises: this gives a simple but effective decision procedure for IPC.

### Abduction in Logic Programming

- Computer ScienceComputational Logic: Logic Programming and Beyond
- 2002

This paper aims to chart out the main developments of the field over the last ten years and to take a critical view of these developments from several perspectives: logical, epistemological, computational and suitability to application.