Skip to content


Switch branches/tags

Name already in use

A tag already exists with the provided branch name. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Are you sure you want to create this branch?

Latest commit


Git stats


Failed to load latest commit information.
Latest commit message
Commit time


A set of tools to semantically embed (multi-modal) higher-order modal logic problems formulated in the TPTP [1] dialect THF into higher-order logic formulated in THF. It contains

  • a standalone tool embed for the semantical embedding.
  • a conversion tool convert_qmltp_to_thf for translating first-order modal logic problems formulated in the dialect of the QMLTP [2] to higher-order logic problems formulated in THF. A translated version of the QMLTP can be found on Github [3].
  • a library embedding_lib you can include in your project to semantically embed problems. Contains wrapper functions for easier handling.

This software is based on the theoretical work of Benzmüller and Paulson [4].

Details of the embedding's procedure, a theoretical overview and some performance tests are available in Gleißner, Steen and Benzmüller [5].


  • Maven 3.5 or higher
  • Java 8 or higher
  • Make


In the root directory invoke

mvn clean package


Converting a problem

To convert a modal problem run

java -jar embed/target/embed-1.0-SNAPSHOT-shaded.jar 

Converting a directory

To recursively convert a directory containing modal problems run

java -jar embed/target/embed-1.0-SNAPSHOT-shaded.jar 
-diroutput <OUTPUT_OPTIONS>

This will preserve the directory structure in the output. If more than semantic is specified the choices for <OUTPUT_OPTIONS> become relevant:

  • joint: exactly one duplicate directory structure and filenames contain a string representing the semantics used during the embedding
  • splitted: one duplicate directory structure for every semantic

Adding Semantics

Specify semantics (which overrides any semantics specified in the problem) for mono-modal problems using

-consequences <CONSEQUENCES>
-constants <CONSTANTS>
-domains <DOMAINS>
-systems <SYSTEMS>

Valid choices for the semantics parameters are

  • <CONSEQUENCES>: global,local
  • <CONSTANTS>: rigid
  • <DOMAINS>: constant, cumulative, decreasing, varying
  • <SYSTEMS>: K, KB, K4, K5, K45, KB5, KB5_KB5, KB5_KB4, D, DB, D4, D5, D45, T, B, S4, S5, S5_KT5, S5_KTB5, S5_KT45, S5_KT4B, S5_KD4B, S5_KD4B5, S5_KDB5, S5U

Note that systems with the same prefix are different axiomatizations of the same semantics.

Specify multiple semantics that creates multiple embedded problems by separating the parameters with a comma e.g.

-domains constant,cumulative

This will create embeddings for all semantics contained by the cross-product of <CONSEQUENCES> x <CONSTANTS> x <DOMAINS> x <SYSTEMS>

Transformation Parameters

Specify special parameters using


Valid choices for <OPTIONS> are

  • semantical_modality_axiomatization: embed modality semantics as frame conditions
  • syntactical_modality_axiomatization: embed modality semantics as axioms about modal operators


[1] Geoff Sutcliffe - The TPTP Problem Library and Associated Infrastructure. From CNF to TH0, TPTP v6.4.0 - 2017 - Journal of Automated Reasoning -

[2] Thomas Raths and Jens Otten - The QMLTP Problem Library for First-Order Modal Logics - 2012 - Automated Reasoning, IJCAR 2012 - -

[3] Tobias Gleißner - QMLTP Mirror and QMLTP in THF -

[4] Christoph Benzmüller and Lawrence C. Paulson - Quantified Multimodal Logics in Simple Type Theory - 2013 - Logica Universalis (Special Issue on Multimodal Logics) -

[5] Tobias Gleißner, Alexander Steen and Christoph Benzmüller - Theorem Provers For Every Normal Modal Logic - 2017 - LPAR-21. 21st International Conference on Logic for Programming, Artificial Intelligence and Reasoning -


A tool for translating higher-order modal logic problems into classical higher-order logic








No packages published