Supervisory Control of (max,+) Automata: A Behavioral Approach

A behavioral framework for control of (max,+) automata is proposed. It is based on behaviors (formal power series) and a generalized version of the Hadamard product, which is the behavior of a generalized tensor product of the plant and controller (max,+) automata in their linear representations. In the tensor product and the Hadamard product, the uncontrollable events that can neither be disabled nor delayed are distinguished. Supervisory control of (max,+) automata is then studied using residuation theory applied to our generalization of the Hadamard product of formal power series. This yields a notion of controllability of formal power series as well as (max,+)-counterparts of supremal controllable languages. Finally, rationality as an equivalent condition to realizability of the resulting controller series is discussed together with hints on future use of this approach

Semantic Process Modeling – Design and Implementation of an Ontology-based Representation of Business Processes

An extension of process modeling languages is designed which allows representing the semantics of model element labels which are formulated in natural language by using concepts of a formal ontology. This combination of semiformal models with formal ontologies will be characterized as semantic process modeling. The approach is exemplarily applied to the languages EPC (Event-driven Process Chain), BPMN (Business Process Modeling Notation) and OWL (Web Ontology Language) and is generalized by means of an information model. The proposed formalization of the semantics of individual model elements in conjunction with the usage of inference engines allows the improvement of query functionalities in modeling tools and enables new possibilities of model validation. The integration of the approach in the IT-based work environments of modelers is demonstrated by a system architecture and a prototypical implementation. Evidently, advantages in the areas of modeling, model management, IT-business alignment, and compliance can be achieved by the application of modeling tools augmented with semantic technologies

Meta-Reasoning: Semantics-Symbol Deconstruction For Large Language Models

Neural-symbolic methods have shown their effectiveness in enhancing the reasoning abilities of large language models (LLMs). However, existing methods primarily rely on mapping natural languages to more syntactically complete formal languages (e.g., Python and SQL). Those approaches necessitate that reasoning tasks be convertible into programs, which cater more to the computer execution mindset and deviate from human reasoning habits. To expand the real-world applicability and flexibility of symbolic methods, we propose Meta-Reasoning from the scope of linguistics itself. This method empowers LLMs to deconstruct questions and effectively capture more generalized knowledge autonomously. We find that Meta-Reasoning achieves improved in-context learning efficiency, reasoning accuracy, and output stability in six arithmetic and symbolic reasoning tasks. In particular, when applied to symbolic reasoning tasks such as Tracking Shuffled Objects, GPT-3 (text-davinci-002) surpasses the few-shot Chain-of-Thought prompting approach (+37.7%), with 99% accuracy after a single demonstration of Meta-Reasoning.Comment: Work in progres

Monoid automata for displacement context-free languages

In 2007 Kambites presented an algebraic interpretation of Chomsky-Schutzenberger theorem for context-free languages. We give an interpretation of the corresponding theorem for the class of displacement context-free languages which are equivalent to well-nested multiple context-free languages. We also obtain a characterization of k-displacement context-free languages in terms of monoid automata and show how such automata can be simulated on two stacks. We introduce the simultaneous two-stack automata and compare different variants of its definition. All the definitions considered are shown to be equivalent basing on the geometric interpretation of memory operations of these automata.Comment: Revised version for ESSLLI Student Session 2013 selected paper

A Formal Model of Metaphor in Frame Semantics

A formal model of metaphor is introduced. It models metaphor, first, as an interaction of “frames” according to the frame semantics, and then, as a wave function in Hilbert space. The practical way for a probability distribution and a corresponding wave function to be assigned to a given metaphor in a given language is considered. A series of formal definitions is deduced from this for: “representation”, “reality”, “language”, “ontology”, etc. All are based on Hilbert space. A few statements about a quantum computer are implied: The sodefined reality is inherent and internal to it. It can report a result only “metaphorically”. It will demolish transmitting the result “literally”, i.e. absolutely exactly. A new and different formal definition of metaphor is introduced as a few entangled wave functions corresponding to different “signs” in different language formally defined as above. The change of frames as the change from the one to the other formal definition of metaphor is interpreted as a formal definition of thought. Four areas of cognition are unified as different but isomorphic interpretations of the mathematical model based on Hilbert space. These are: quantum mechanics, frame semantics, formal semantics by means of quantum computer, and the theory of metaphor in linguistics

Algebraic Aspects of Families of Fuzzy Languages

We study operations on fuzzy languages such as union, concatenation, Kleene $\star$, intersection with regular fuzzy languages, and several kinds of (iterated) fuzzy substitution. Then we consider families of fuzzy languages, closed under a fixed collection of these operations, which results in the concept of full Abstract Family of Fuzzy Languages or full AFFL. This algebraic structure is the fuzzy counterpart of the notion of full Abstract Family of Languages that has been encountered frequently in investigating families of crisp (i.e., non-fuzzy) languages. Some simpler and more complicated algebraic structures (such as full substitution-closed AFFL, full super-AFFL, full hyper-AFFL) will be considered as well.\ud In the second part of the paper we focus our attention to full AFFL's closed under iterated parallel fuzzy substitution, where the iterating process is prescribed by given crisp control languages. Proceeding inductively over the family of these control languages, yields an infinite sequence of full AFFL-structures with increasingly stronger closure properties