A Cognitively-Inspired Model for Making Sense of Hasse Diagrams

In this paper, we present a model of the sense-making process for diagrams, and describe it for the case of Hasse diagrams. Sense-making is modeled as the construction of networks of conceptual blends among image schemas and the diagram’s geometric configuration. As a case study, we specify four image schemas and the geometric configuration of a Hasse diagram, with typed FOL theories. In addition, for the diagram geometry, we utilise Qualitative Spatial Reasoning formalisms. Using an algebraic specification language, we can compute conceptual blends as category-theoretic colimits. Our model approaches sense-making as a process where the image schemas and the diagram geometry both structure each other through a complex network of conceptual blends. This yields a final blend in which the sort of inferences we confer to diagrammatic representations emerge. We argue that this approach to sense-making in diagrams is more cognitively apt than the mainstream view of a diagram being a syntactic representation of some underlying logical semantics. Moreover, our model could be applied to various types of stimuli and is thus valuable for the general field of AI.

Solving Syllogisms as Abstract Pattern Recognition and Completion, Based on Linguistic Cues for Logical Semantic Features

The presented empirical research is based on a new model for the categorical syllogisms, described and partially tested elsewhere. This model assumes that deriving a conclusion involves a pattern completion process, similar to the completion of perceptual patterns. Specifically, inferring a conclusion would require the generation of the missing part of an abstract pattern of logical semantic features. This pattern is named schema, because it is organized around a particular argumentative goal. Such a schema emerges through the frequent contact with a corresponding class of argumentative experiences. As, presumably, the usual pragmatic argumentative contexts imply predominantly valid syllogisms, pragmatic syllogistic schemas would emerge mainly for them. These pragmatic schemas for the valid syllogisms are supposed to be based on a particular mixed semantics of their syllogistic judgments, including both intensional (class-property) and extensional (subclass-class) relationships. The recognition of these schemas can be influenced by the linguistic cues of the verbal expression of the syllogisms. To test this particular prediction, the linguistic format of a set of 24 abstract categorical syllogisms (12 valid, 12 invalid) was varied. The linguistic cues of the L format task would favor the recognition of the logical features of the assumed syllogistic schemas with a mixed logical semantics of the valid syllogisms. The N format task, with no explicit linguistic cues for those logical features, would hinder the recognition of the above-mentioned schemas for the valid syllogisms. The administration order of the two tasks was also varied. The study included 192 university students. The data supported considerably the expected format effects on the correctness of the chosen answers for the valid syllogisms (with higher performances for the L format) in the relevant between-subjects and within-subjects comparisons, and some of the predicted order effects. Mental models theory cannot explain the obtained results.

Adapting Logic to Physics: The Quantum-Like Eigenlogic Program

Considering links between logic and physics is important because of the fast development of quantum information technologies in our everyday life. This paper discusses a new method in logic inspired from quantum theory using operators, named Eigenlogic. It expresses logical propositions using linear algebra. Logical functions are represented by operators and logical truth tables correspond to the eigenvalue structure. It extends the possibilities of classical logic by changing the semantics from the Boolean binary alphabet { 0 , 1 } using projection operators to the binary alphabet { + 1 , − 1 } employing reversible involution operators. Also, many-valued logical operators are synthesized, for whatever alphabet, using operator methods based on Lagrange interpolation and on the Cayley–Hamilton theorem. Considering a superposition of logical input states one gets a fuzzy logic representation where the fuzzy membership function is the quantum probability given by the Born rule. Historical parallels from Boole, Post, Poincaré and Combinatory Logic are presented in relation to probability theory, non-commutative quaternion algebra and Turing machines. An extension to first order logic is proposed inspired by Grover’s algorithm. Eigenlogic is essentially a logic of operators and its truth-table logical semantics is provided by the eigenvalue structure which is shown to be related to the universality of logical quantum gates, a fundamental role being played by non-commutativity and entanglement.

Functorial Model Management

In this paper we use formal tools from category theory to develop a foundation for creating and managing models in systems where knowledge is distributed across multiple representations and formats. We define a class of models which incorporate three different representations---computations, logical semantics, and data--as well as model mappings (functors) to establish relationships between them. We prove that our models support model merge operations called colimits and use these to define a methodology for model integration.

Differentiating scalar implicature from exclusion inferences in language acquisition

During acquisition, children must learn both the meanings of words and how to interpret them in context. For example, children must learn the logical semantics of the scalar quantifier some and its pragmatically enriched meaning: ‘some but not all’. Some studies have shown that ‘scalar implicature’ – that some implies ‘some but not all’ – poses a challenge even to nine-year-olds, while others find success by age three. We asked whether reports of children's successes might be due to the computation of exclusion inferences (like contrast or mutual exclusivity) rather than scalar implicatures. We found that young children (N = 214; ages 4;0–7;11) sometimes compute symmetrical exclusion inferences rather than asymmetric scalar inferences. These data suggest that a stronger burden of evidence is required in studies of implicature; before concluding that children compute implicatures, researchers should first show that children exhibit sensitivity to asymmetric entailment in the task.

Interoperability in Smart Manufacturing: Research Challenges

Recent advances in manufacturing technology, such as cyber–physical systems, industrial Internet, AI (Artificial Intelligence), and machine learning have driven the evolution of manufacturing architectures into integrated networks of automation devices, services, and enterprises. One of the resulting challenges of this evolution is the increased need for interoperability at different levels of the manufacturing ecosystem. The scope ranges from shop–floor software, devices, and control systems to Internet-based cloud-platforms, providing various services on-demand. Successful implementation of interoperability in smart manufacturing would, thus, result in effective communication and error-prone data-exchange between machines, sensors, actuators, users, systems, and platforms. A significant challenge to this is the architecture and the platforms that are used by machines and software packages. A better understanding of the subject can be achieved by studying industry-specific communication protocols and their respective logical semantics. A review of research conducted in this area is provided in this article to gain perspective on the various dimensions and types of interoperability. This article provides a multi-faceted approach to the research area of interoperability by reviewing key concepts and existing research efforts in the domain, as well as by discussing challenges and solutions.

Translation Analysis of Taxis in “The Old Man and the Sea” Novel (Systemic Functional Linguistics Approach)

The Old Man and the Sea is a literature work by Ernest Hemingway. It has been translated into many languages even in Indonesian by Deera Army. Hemingway used more clause complex in producing his works. It causes problems in translation such as: translators should give more attention to the translation techniques used, readability decrease, and etc. On the other hand, Deera Army solved those problems by splitting the clause complex into shorter one. It is needed to conduct a study in how to make translation of complex clause. This study can be clearly conducted by using Systemic Functional Grammar (SFG) approach. In addition, this study is aimed at: (1) describing how can be interdependency and logical semantics of complex clause in source language realized into interdependency and logical semantics of complex clause in target language of The Old Man and the Sea Novel (2) describing what translation techniques on taxis markers are used in translating from source language to target language (3) describing translation quality of clause complex translation in target language. The result of the analysis showed that there are 400 sentences which have been broken into 701 clauses. Based on the analysis, there are paratactic and hypotactic form. Paratactic took 65.30% and hypotactic, 34.50%. All of them affect translation quality. Based on the analysis, the average of accuration takes up 2.89, naturalness with 2.96 and readibility with 2.97. The writer suggests that the next researcher can conduct the same research in the deeper way.

Type-logical semantics

Type-logical semantics studies linguistic meaning with the help of the theory of types. The latter originated with Russell as an answer to the paradoxes, but has the additional virtue that it is very close to ordinary language. In fact, type theory is so much more similar to language than predicate logic is, that adopting it as a vehicle of representation can overcome the mismatches between grammatical form and predicate logical form that were observed by Frege and Russell. The grammatical forms of ordinary language sentences consequently may be taken to be much less misleading than logicians in the first half of the twentieth century often thought them to be. This was realized by Richard Montague, who used the theory of types to translate fragments of ordinary language into a logical language. Semantics is commonly divided into lexical semantics, which studies the meaning of words, and compositional semantics, which studies the way in which complex phrases obtain a meaning from their constituents. The strength of type-logical semantics lies with the latter, but type-logical theories can be combined with many competing hypotheses about lexical meaning, provided these hypotheses are expressed using the language of type theory.

Bolzano, Bernard (1781–1848)

Bernard Bolzano was a lone forerunner both of analytical philosophy and phenomenology. Born in Prague in the year when Kant’s first Critique appeared, he became one of the most acute critics both of Kant and of German Idealism. He died in Prague in the same year in which Frege was born; Frege is philosophically closer to him than any other thinker of the nineteenth or twentieth century. Bolzano was the only outstanding proponent of utilitarianism among German-speaking philosophers, and was a creative mathematician whose name is duly remembered in the annals of this discipline. His Wissenschaftslehre (Theory of Science) of 1837 makes him the greatest logician in the period between Leibniz and Frege. The book was sadly neglected by Bolzano’s contemporaries, but rediscovered by Brentano’s pupils: Its ontology of propositions and ideas provided Husserl with much of his ammunition in his fight against psychologism and in support of phenomenology, and through Twardowski it also had an impact on the development of logical semantics in the Lwów-Warsaw School.