Abstract Often philosophers, logicians, and mathematicians employ a notion of intended structure when talking about branch mathematics. In addition, we know that there are foundational mathematical theories can find representatives for the objects informal this paper, examine how faithfully represent structures, show question is closely linked to decidability theory structure. We argue sheds li...

Proof-theory has traditionally been developed based on linguistic (symbolic) representations of logical proofs. Recently, however, logical reasoning based on diagrammatic or graphical representations has been investigated by logicians. Euler diagrams were introduced in the 18th century by Euler [1768]. But it is quite recent (more precisely, in the 1990s) that logicians started to study them fr...

There is a wide gulf between the formal logics used by logicians to describe agents and the informal vocabulary used by people who actually build robotic agents. In an effort to help bridge the gap, this paper applies techniques borrowed from the field of formal software methods to develop a common vocabulary. Terms useful for discussing agents are given formal definitions. A framework for desc...

Aristotle (384–322 BC), the founder of the discipline of logic, also founded the study of quantification. Normally, Aristotle begins a topic by reviewing the common opinions, including the opinions of his chief predecessors. In logic, however, he could not adopt the same strategy; before him, he reports, “there was nothing at all” (Sophistical Refutations 183b34–36). Aristotle’s theory dominate...

In knowledge representation and reasoning systems, diagrams have many practical applications and are used in numerous settings. Indeed, it is widely accepted that diagrams are a valuable aid to intuition and help to convey ideas and information in a clear way. On the other side, logicians have viewed diagrams as informal tools, but which cannot be used in the manner of formal argumentation. Ins...

N.B.: For the references, please see Selected Bibliography on Aristotle's Theory of Categorical Syllogism "When modem logicians in the 1920s and 1930s first turned their attention to the problem of understanding Aristotle’s contribution to logic in modern terms, they were guided both by the Frege-Russell conception of logic as formal ontology and at the same time by a desire to protect Aristotl...

This paper is a contribution to natural logic, the study of logical systems for linguistic reasoning. We construct a system with the following properties: its syntax is closer to that of a natural language than is first-order logic; it can faithfully represent simple sentences with standard quantifiers, subject relative clauses (a recursive construct), and negation on nouns and verbs. We also g...

A concern of the organizers of the workshop on ‘Games, Action and Social Software’ is that although everyone is keen to use logic for the analysis of key concepts in this area, it is not so clear which logic or which tools from logic to use for investigating games, actions and social software. For this reason, they have organized a discussion session on the theme “Battle of the Logics: Temporal...