# Teaching the Formalization of Mathematical Theories and Algorithms via the Automatic Checking of Finite Models

@inproceedings{Schreiner2017TeachingTF, title={Teaching the Formalization of Mathematical Theories and Algorithms via the Automatic Checking of Finite Models}, author={Wolfgang Schreiner and Alexander Brunhuemer and Christoph F{\"u}rst}, booktitle={ThEdu@CADE}, year={2017} }

Education in the practical applications of logic and proving such as the formal specification and verification of computer programs is substantially hampered by the fact that most time and effort that is invested in proving is actually wasted in vain: because of errors in the specifications respectively algorithms that students have developed, their proof attempts are often pointless (because the proposition proved is actually not of interest) or a priori doomed to fail (because the proposition…

## 12 Citations

### Theorem and Algorithm Checking for Courses on Logic and Formal Methods

- Computer ScienceThEdu@FLoC
- 2018

Some new enhancements of the RISC Algorithm Language are reported on: the automatic generation of checkable verification conditions from algorithms, the visualization of the execution of procedures and the evaluation of formulas illustrating the computation of their results, and the generation of Web-based student exercises and assignments from RISCAL specifications.

### Mathematical Model Checking Based on Semantics and SMT

- Computer Science
- 2021

RISCAL, a model checker for mathematical theories and algorithms based on a variant of first-order logic with finite models, is reported on, which allows to automatically decide the validity of all formulas and to verify the correctness of all algorithms specified by such formulas.

### The RISC Algorithm Language ( RISCAL ) Tutorial and Reference Manual ( Version 1 . 0 . 17 )

- Computer Science
- 2017

This report documents the RISC Algorithm Language, a language and associated software system for describing (potentially nondeterministic) mathematical algorithms over discrete structures that implements a model checker that allows to verify the correctness of algorithms and the associated theories with respect to their specifications for all possible input values of the parameter domains.

### Validating Mathematical Theorems and Algorithms with RISCAL

- Computer ScienceCICM
- 2018

This work aims to quickly detect errors respectively inadequacies in the formalization by falsification in small model instances before attempting actual correctness proofs for the whole model class.

### Logic and Semantic Technologies for Computer Science Education

- Computer Science2019 IEEE 15th International Scientific Conference on Informatics
- 2019

The experience with the RISCAL software, a model checker for mathematical theories and algorithms, in university courses on logic, formal methods, and formal modeling is described.

### Semantic Evaluation versus SMT Solving in the RISCAL Model Checker

- Computer Science
- 2021

These investigations also identify some classes of formulas where semantic evaluation is able to compete with (or even outperform) satisfiability solving, outlining some room for improvements in the translation of RISCAL formulas to SMT-LIB formulas as well as in the current SMT technology.

### Prototyping "Systems that Explain Themselves" for Education

- Computer ScienceThEdu@CADE
- 2017

By the way of describing the process of prototyping the first comprehensive survey on the state of the ISAC prototype is given as a side effect, made precise by pointers to the code and by citation of all contributing theses.

### A Categorical Semantics of Relational First-Order Logic∗

- Computer Science
- 2019

The focus is to show how the semantics of first order formulas can be derived from their usual deduction rules, by modeling the categorical semantics in the RISCAL (RISC Algorithm Language) system which allows the core propositions by automatically checking them in finite models.

### A Novel Categorical Approach to Semantics of Relational First-Order Logic

- Computer ScienceSymmetry
- 2020

This paper shows how the semantics of first-order formulas can be derived from their usual deduction rules by modeling the categorical semantics in the RISCAL (RISC Algorithm Language) system which allows us to validate the core propositions by automatically checking them in finite models.

### Visualizing Logic Formula Evaluation in RISCAL∗

- Computer Science
- 2018

The visualization of the evaluation of logic formulas that are formulated in the RISC Algorithm Language consists of a pruned evaluation tree that depicts exactly those evaluation branches that contribute to the overall truth value of a formula.

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This report documents the RISC Algorithm Language, a language and associated software system for describing (potentially nondeterministic) mathematical algorithms over discrete structures that implements a model checker that allows to verify the correctness of algorithms and the associated theories with respect to their specifications for all possible input values of the parameter domains.

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