Logical conditions in programming languages: review, discussion and generalization

Symbolic logic can be used to translate verbal statements of the optimization problem into an exact mathematical form. There are then three stages in the problem formulation—the verbal stage, the logical stage and the mathematical stage. The purpose of this paper is to translate statements of symbolic logic into the language of zero-one linear programming. Concepts of symbolic logic and zero-one linear programming will be described with examples of translating verbal statements into symbolic logic, and of translating logical statements into a mathematically equivalent form.

A programming language is an intermediate medium between the human user and the machine. Ideally it should reduce the gap between human reasoning and the machine's processing mechanism to the minimum. Accordingly, none of the contemporaryprogramming languages can be said to be ideal. Prolog is no exception. However, it is usually emphasized that programming in Prolog is very easy, even a beginner can handle it within a few hours of learning. The rationale behind this conception is that Prolog clauses are actually some logical statements, and logic is the basis of every rational subject. The problem arises in that Prolog programming is not equivalent to logic programming. Prolog still shares the effect of the influence of the fundamental Von Neumann computer architecture on conventional programming languages. If a user wants to write a Prolog program just according to his logical reasoning, he will probably fall into an unexpected trap of the language.

Two studies were conducted to examine the use of grounded embodied pedagogy, construction of Imaginary Worlds (Study 1), and context of instructional materials (Study 2) for developing learners' Computational Thinking (CT) Skills and Concept knowledge during the construction of digital artifacts using Scratch, a block-based programming language. Utilizing a conceptual framework for grounded embodied pedagogy called Instructional Embodiment, learners physically enacted (Direct Embodiment) and mentally simulated (Imagined Embodiment) the actions and events as presented within pre-defined Scripts. Instructional Embodiment utilizes action, perception, and environment to create a dynamic, interactive teaching & learning scenario that builds upon previous research in embodied teaching and learning. The two studies described herein examined the effects of Instructional Embodiment, Imaginary World Construction, and Context on the development of specific Computational Thinking Concepts and Skills. In particular, certain CT Concepts, such as Conditionals, Variables, Thread Synchronization, Collision Detection, & Events, and CT Skills, such as abstraction and pattern recognition, were identified and measured within the learners' individual digital artifacts. Presence and/or frequency of these Concepts and Skills were used to determine the extent of Computational Thinking development. In Study 1, fifty-six sixth- and seventh-grade students participated in a fifteen-session curricular program during the academic school day. This study examined the type of instruction and continuity of Imaginary World Construction on the development of certain CT Skills and Concepts used in a visual novel created in Scratch. Main effects were found for learners who physically embodied the pre-defined instructional materials: embodying the pre-defined Scripts led to the learners using significantly more ‘speech’ Blocks in their projects and more Absolute Positioning Blocks for ‘motion’ than those who did not physically embody the same Scripts. Significant main effects were also found for continuity of Imaginary World Construction: learners who were instructed to continue the premise of the first digital artifact (Instructional Artifact) implemented significantly more computational structures in their second digital artifact (Unique Artifact) than those who were instructed to create a Unique Artifact with a premise of their own design. In Study 2, seventy-eight sixth- and seventh-grade students participated in a seventeen-session curricular program during the academic school day. This study examined the type of instruction and context of instructional materials on the development of CT Skills and Concepts during the construction of a video game using Scratch. Similar to Study 1, findings suggest that physically embodying the actions presented within the pre-defined instructional materials leads to greater implementation of many of these same structures during individual artifact construction. The study also showed that as the pre-defined Scripts become more complex (e.g. single-threaded to multi-threaded), the effect of physical embodiment on the development of CT Skills and complex CT Concept structures becomes less pronounced. Findings from this study also suggest that Context has a significant effect on identifying & implementing the CT Skill pattern recognition: learning CT Concepts from an Unfamiliar Context had a significant positive effect on the implementation of both Broadcast/Receive couplings and Conditional Logic & Operator patterns. In sum, the findings suggest that the type of instruction, the continuity of the Imaginary World being constructed, and the context of the instructional materials all play a significant role in the learners' ability to develop certain Computational Thinking Skills and Concept knowledge. The findings also suggest that a physically embodied approach to teaching abstract concepts that is grounded in an unfamiliar context is the most effective way to integrate a grounded embodied approach to pedagogy within a formal instructional setting.

A GRAPH-THEORETIC PROGRAMMING LANGUAGE