Logical Studies

Abstract One of the questions in ontological pluralism is whether or not to accept the generic quantifier. But if we accept the generic quantifier due to reasons that are for the acceptance of the generic quantifier, then ontological pluralism will face problems due to other reasons, for example, it is as if pluralism and monism are just notationally variant of each other and there is no genuine and important difference between them. In other words, the acceptance of generic quantifier offers a kind of monistic counterpart for pluralism, and this monistic counterpart causes three basic problems for pluralism. Of course, these three problems are considered to be one of the most important criticisms of ontological pluralism. In the following article, these three problems are discussed. After clarifying each of them, we have criticized and rejected them. Our key in rejecting these three problems is the assumption that the generic quantifier is not an elite and fundamental quantifier and can only be defined based on restricted quantifiers. Therefore, it has been shown that ontological pluralism, if accepts the generic quantifier and if it does not consider this generic quantifier as elite, it will not face any problem.

Abstract Different kinds of nonstandard conditionals of modal nature, are studied in conditional logic or Dyadic Modal Logic. Preference structures are one of the important categories of semantic models for these logics. Deontic conditionals and nonmonotonic conditionals are two kinds of these nonstandard conditionals, such that these models have been introduced as one of their main semantics.
In this paper we have a brief review of the literature of preference models in these two branches. Then we compare the subjects studied under the topic of preference models in both fields and have an analysis about the meaning and the acceptance of the axioms of conditional logics, when the conditionals either read as deontic conditionals or as nonmonotonic ones.
In addition, we present some examples to show that in the both fields, preference models have shortcomings in expressing the correct and intuitive reasoning. We offer some extended semantics from nonmonotonic literature to overcome these shortcomings.

Abstract The logic {LP} is a paraconsistent logic that bears strong structural and semantic similarities to the LP logic introduced by Graham Priest. It is defined using Nmatrices, a semantic tool that plays a significant role in the study of paraconsistent logics by allowing for the analysis of contradictory statements without collapsing the entire logical system. In this paper, we first present the semantic framework of this logic and then develop a proof theory for it based on Gentzen-type sequent calculus. We show that this proof system is both sound and complete with respect to the proposed matrix semantics. Another focus of this study is the analysis of certain distinctive features of the {LP} logic, where noticeable differences from the original LP logic emerge. In particular, we examine the non-standard behavior of the conjunction operator in this logic, which functions in such a radically different way from common logics that the term “conjunction” barely seems appropriate.

Abstract Counterfactual emotions, such as envy and regret, play a foundational role in shaping human behavior, influencing moral judgment, and guiding social interaction. Because they arise from the comparison between actual states and imagined alternative scenarios, these emotions serve as powerful cognitive mechanisms that motivate individuals to reassess their decisions, modify their actions, and anticipate future consequences. Consequently, they are of substantial importance to the advancement of research in artificial intelligence and multi-agent systems, where modeling human-like affective reasoning remains a central challenge. In this article, we formalize the counterfactual emotions of envy and regret using the Counterfactual Emotions (CFE) framework [2]. Furthermore, we examine their intensity through quantitative constructs such as the “degree of importance,” “degree of inadequacy,” and “degree of counterfactual avoidability” introduced in [1]. This study provides a theoretical and computational foundation for developing intelligent agents capable of understanding, representing, and adapting to the complex emotional and ethical dimensions of human interaction.

Abstract The present article is one of the first written in the Western world on the relationship between logic and ontology (or metaphysics in general). Bocheński shows that Gottlob Frege, the father of mathematical logic, by placing truth instead of inference as the subject matter of logic, brought logic very close to ontology and metaphysics, to the point that some of Frege's followers, such as Heinrich Scholz, considered logic and ontology to be one and the same. On the other hand, of course, a group such as Ernest Nagel remained faithful to tradition and considered logic and ontology to be completely distinct from each other. In explaining this historical controversy on the relationship between logic and ontology, Bocheński points out that the roots of this controversy are in Aristotle's two books on syllogisms and polemics (originally titled Prior Analytics and Topics). In Prior Analytics, Aristotle expresses his logical results (i.e., the moods of syllogism) in the form of truths and laws, while in Topics, he had proposed logical results in the form of rules of debate and of dialogue between two opponents (the questioner and the answerer). Bocheński claims that the logical tradition after Aristotle, from the Stoics to before modern logic, all saw logic in the form of Aristotele’s Topics, i.e. as rules of debate and dialogue, unlike mathematical logicians such as Leibniz, George Boole, and Frege, who saw logic in the form of Aristotele’s Prior Analytics, i.e. as axioms and laws.