Software Tools in Logic Education: Some Examples

Computers are increasingly present in education and make manyresources and activities available to teachers and pupils. Newpedagogical resources development is very interesting for both.Our digital library Summa Logicae is overtly involved in innovationand pedagogical systematization. It includes some software toolsfor teaching logic developed by computer science students, andin this article we present two of these tools. The MAFIA toolis especially attractive for first year students and helps themto understand the basic concepts of logic in an interactiveway using sematic tableaux. It also allows them to solve thecrazy cases in Mafia which their fellow students from previousyears proposed. The Modelos de Kripke tool, oriented to a moreadvanced level, serves for understanding the link between theproperties of the accessibility relation and the modal formulas,which is at the basis of the current developments of modal logic.     

Term-Modal Logics

Many powerful logics exist today for reasoning about multi-agent systems, but in most of these it is hard to reason about an infinite or indeterminate number of agents. Also the naming schemes used in the logics often lack expressiveness to name agents in an intuitive way.To obtain a more expressive language for multi-agent reasoning and a better naming scheme for agents, we introduce a family of logics called term-modal logics. A main feature of our logics is the use of modal operators indexed by the terms of the logics. Thus, one can quantify over variables occurring in modal operators. In term-modal logics agents can be represented by terms, and knowledge of agents is expressed with formulas within the scope of modal operators.This gives us a flexible and uniform language for reasoning about the agents themselves and their knowledge. This article gives examples of the expressiveness of the languages and provides sequent-style and tableau-based proof systems for the logics. Furthermore we give proofs of soundness and completeness with respect to the possible world semantics.