Relating Semantics for Epistemic Logic

The aim of this paper is to explore the advantages deriving from the application of relating semantics in epistemic logic. As a first step, I will discuss two versions of relating semantics and how they can be differently exploited for studying modal and epistemic operators. Next, I consider several standard frameworks which are suitable for modelling knowledge and related notions, in both their implicit and their explicit form and present a simple strategy by virtue of which they can be associated with intuitive systems of relating logic. As a final step, I will focus on the logic of knowledge based on justification logic and show how relating semantics helps us to provide an elegant solution to some problems related to the standard interpretation of the explicit epistemic operators.

Principles of epistemic logic I: Knowledge

All epistemic logics come with some idealizations. Not all such idealizations seem acceptable. A large family of epistemic logics assume that if ⌜φ‎⌝ and ⌜ψ‎⌝ are logically equivalent, so are ⌜One knows that φ‎⌝ and ⌜One knows that ψ‎⌝. This assumption, characteristic of normal epistemic logics but also of many non-normal ones, is acceptable only if the objects of knowledge can be construed as sets of possible worlds known under some mode of presentation or other, where knowledge-ascriptions do not yet make those modes explicit. Unlike fine-grained conceptions that reject the assumption, such coarse-grained conceptions of the objects of knowledge have the untoward consequence that failures of logical omniscience are no longer expressible in the logic. But even on coarse-grained conceptions, epistemic logic cannot be expected to be normal. Fine-grained conceptions allow for failures of logical omniscience to be expressible in the logic. On balance, fine-grained conceptions are to be preferred. Against this backdrop, candidate principles for inclusion in the logic of knowledge are critically reviewed in the light of general epistemological considerations. Very few survive closer scrutiny.

A logic of knowledge based on abstract arguments

We introduce a logic of knowledge in a framework in which knowledge is treated as a kind of belief. The framework is based on a standard KD45 characterization of belief, and the characterization of knowledge undergoes the classical tripartite analysis that knowledge is justified true belief, which has a natural link to the studies of logics of evidence and justification. The interpretation of knowledge avoids the unwanted properties of logical omniscience, independent of the choice of the base logic of belief. We axiomatize the logic, prove its soundness and completeness and study the computational complexity results of the model checking and satisfiability problems. We extend the logic to a multi-agent setting and introduce a variant in which belief is characterized in a weaker system to avoid the problem of logical omniscience.

Max Weber on Science, in the Context of Our Days Thinking

Max Weber analyzes the science of the Modern Period. The revolution in physics at the beginning of the 20th century, the creation of quantum mechanics bring to the fore another type of scientific thinking. It is important to note that past knowledge in this case is not refuted, not destroyed, it becomes marginal and enters into communication with its competitor. It is this type of communication with Weber’s philosophy of scientific thinking that helps us to understand its specificity. According to Weber, new knowledge is derived from the previous one, refuting its truth. On this basis, Weber writes that science is different from the art, where the created works retain their significance regardless of the time when they were created. For modern science the predecessor is necessary as another, without which not any communication is possible. Classical science, about which Weber writes, is necessary and continues to function. Satisfying the reemerging needs of society, it can detect previously hidden possibilities and, at the same time, encourage new scientific thinking to strengthen its position.The concept of revolution disappears gradually from the works on science. Instead, sociological concepts such as an innovation center or a technopark that combine simultaneously changes in the logic of knowledge and in the technical equipment of society are becoming popular. Logical and social characteristics of science are combined, the boundary between them becomes less noticeable. If in the era of classics the artificial world surrounding man was built on the basis of the laws of nature, now it is being created on the basis of the laws of thinking. For Weber, this world was silent and dead, this is what classical science testified to. Now the world around us is endowed with artificial intelligence, and we must be able to communicate with it. To understand Weber, it is necessary to establish contact with the world of classics, and not to try to destroy it and to declare it worthless.

Situated Embodiment: When Physical Weight Does and Does Not Inform Judgments of Importance

Bodily sensations impact metaphorically related judgments. Are such effects obligatory or do they follow the logic of knowledge accessibility? If the latter, the impact of sensory information should be moderated by the accessibility of the related metaphor at the time of sensory experience. We manipulated whether “importance” was on participants’ minds when they held a physically heavy versus light book. Participants held the book while making an importance judgment versus returned it before making the judgment (Study 1) or learned prior to holding the book that the study was about “importance evaluations” versus “graphics evaluations” (Study 2). In both studies, the same book was judged more important when its heft was increased but only when importance was on participants’ minds at the time of sensory experience. We conclude that sensory experiences only impact metaphorically related judgments when the applicable metaphor is highly accessible at the time of experience.

Vasily Sesemann’s Theory of Knowledge: Intuition, Logic and Dialectic

Nicolai Hartmann interprets the logic of knowledge as a dialectical process that must reveal the processionality of being itself. Sesemann not only extends Hartmann‘s philosophical insights, but also supplements them significantly. He also understands the knowledge of reality not as an analysis of static objects, but as a dynamic and temporal reconstruction of becoming reality. Acknowledging the limitations of intuition, he returns to the possibilities of logically formed knowledge. Sesemann argues that the logical constructions of knowledge must maintain a connection with primal intuition. However, logically formed knowledge is limited by its static nature. A dialectic is needed to reveal a dynamically changing being. I will begin the article by discussing the relationship between intuition and logical knowledge, then examine the problem of the ideal being and conclude by evaluating the significance of dialectics in Sesemann’s theory of knowledge. According to Sesemann, the dialectic, unlike formal logic, must reveal not the ideal laws of thought, but how live knowledge takes place. Dialectics allows one to analyze being as incomplete and indefinite, as becoming and open to infinite change, it allows one to relate a separate aspect of knowledge to the whole.

Situated embodiment: When physical weight does and does not inform judgments of importance

Bodily sensations impact metaphorically related judgments. Are such effects obligatory or do they follow the logic of knowledge accessibility? If the latter, the impact of sensory information should be moderated by the accessibility of the related metaphor at the time of sensory experience. We manipulated whether “importance” was on participants’ minds when they held a physically heavy vs. light book. Participants held the book while making an importance judgment vs. returned it before making the judgment (Study 1) or learned prior to holding the book that the study was about “importance evaluations” vs. “graphics evaluations” (Study 2). In both studies, the same book was judged more important when its heft was increased, but only when importance was on participants’ minds at the time of sensory experience. We conclude that sensory experiences only impact metaphorically-related judgments when the applicable metaphor is highly accessible at the time of experience.