Logicality
In standard model-theoretic semantics, the meaning of logical terms is said to be fixed in the system while that of nonlogical terms remains variable. Much effort has been devoted to characterizing logical terms, those terms that should be fixed, but little has been said on their role in logical systems: on what fixing their meaning precisely amounts to. My proposal is that when a term is considered logical in model theory, what gets fixed is its intension rather than its extension. I provide a rigorous way of spelling out this idea, and show that it leads to a graded account of logicality: the less structure a term requires in order for its intension to be fixed, the more logical it is. Finally, I focus on the class of terms that are invariant under isomorphisms, as they render themselves more easily to mathematical treatment. I propose a mathematical measure for the logicality of such terms based on their associated Löwenheim numbers.
Logicality
When people evaluate syllogisms, their judgments of validity are often biased by the believability of the conclusions of the problems. Thus, it has been suggested that syllogistic reasoning performance is based on an interplay between a conscious and effortful evaluation of logicality and an intuitive appreciation of the believability of the conclusions (e.g., Evans, Newstead, Allen, & Pollard, 1994). However, logic effects in syllogistic reasoning emerge even when participants are unlikely to carry out a full logical analysis of the problems (e.g., Shynkaruk & Thompson, 2006). There is also evidence that people can implicitly detect the conflict between their beliefs and the validity of the problems, even if they are unable to consciously produce a logical response (e.g., De Neys, Moyens, & Vansteenwegen, 2010). In 4 experiments we demonstrate that people intuitively detect the logicality of syllogisms, and this effect emerges independently of participants' conscious mindset and their cognitive capacity. This logic effect is also unrelated to the superficial structure of the problems. Additionally, we provide evidence that the logicality of the syllogisms is detected through slight changes in participants' affective states. In fact, subliminal affective priming had an effect on participants' subjective evaluations of the problems. Finally, when participants misattributed their emotional reactions to background music, this significantly reduced the logic effect.
As mentioned in the comments, the meaning I'm after is "the degree to which something pertains to logic". The same questions can be posed of derivatives of "chronology": for example, if I have a sequence of events and I reorder them so as to make them chronological, did I enforce the chronologicalness, chronologicity, or chronologicality of the sequence?
Logicalness, logicity, and logicality are abstract nouns formed by applying a suffix to the noun logic or the adjective logical. (The process of adding this suffix is suffixation. That word will be relevant in a moment.)
Prince Philip applied a military (or perhaps naval) logicality to all he did. (Hugo Vickers. "Prince Philip - active patron of business organizations and consort to Queen Elizabeth II: Obituary." MarketWatch, 9 April 2021)
To process a huge amount of data, computing resources need to be organized in clusters that can be scaled out easily. Still, traditional SQL databases built on the relational data model are difficult to be put to use in such clusters, which has motivated the movement named NoSQL. However, NoSQL databases have their limits by using their own data models. In this paper, the original soft set theory is extended, and a new theory system called n-tier soft set is brought up. We systematically constructed its concepts, definitions, and operations, establishing it as a novel soft set algebra. And some features of this algebra display its natural advantages as a data model which could combine the logicality of the SQL model (also known as the relational model) and the flexibility of NoSQL models. This data model provides a unified and normative perspective logic for organizing and manipulating data, combines metadata (semantic) and data to form a self-described structure, and combines index and data to realize fast locating and correlating.
We do not compare performance with the current NoSQL databases. As a prototype database implemented in Python, there is no comparability between NTSS and the mature NoSQL database that has evolved for many years in performance. Compared with the current NoSQL database, NTSS has the advantages of query freedom and mathematical logicality. Taking MongoDB as an example, as a popular database, MongoDB is widely applied in everyday applications and has extremely high performance in some queries, but it has no mathematical logicality and cannot query freely (strong at query key to value, but weak at query key to value). So, if you need to get the relationship between the values, it will cost a lot (need index structure or traverse scan). However, the NTSS model is a model with complete mathematical logicality and can query freely between key and value. The NTSS database cannot compete with MongoDB from an implementation perspective because NTSS only stays at the prototype level and will gradually approach the current mainstream NoSQL database through future improvements.
A prominent objection against the logicality of second-order logic is the so-called Overgeneration Argument. However, itis far from clear how this argument is to be understood. In the first part of the article, we examine the argument andlocate its main source, namely the alleged entanglement of second-order logic and mathematics. We then identify variousreasons why the entanglement may be thought to be problematic. In the second part of the article, we take a metatheoretic perspective on the matter. We prove a number of results establishing that the entanglement is sensitive to the kind of semantics used for second-order logic. These results provide evidence that, by moving from the standard set-theoretic semantics for second-order logic to a semantics which makes use of higher-order resources, the entanglement either disappears or may no longer be in conflict with the logicality of second-order logic.
Klauer and Singmann (2013) attempted to replicate an hypothesis of Morsanyi and Handley (2012) according to which individuals have an intuitive sense of logicality. Specifically, Morsanyi and Handley apparently provided evidence that the logical status of syllogisms (i.e., valid or invalid) affects participants liking ratings of the conclusion of syllogisms. Conclusions from valid syllogisms (e.g., Some snakes are poisonous. No poisonous animals are obbs. Some snakes are not obbs.) received higher liking ratings than conclusions from invalid syllogisms (e.g., No ice creams are vons. Some vons are hot. Some ice creams are not hot.). It is important to noted that in the experiments participants were simply shown the premises and conclusion in succession, they were not asked whether or not the conclusion follows or to generate their own conclusion. Their task was simply to judge how much they liked the "final" statement (i.e., the conclusion).
Klauer, K. C., & Singmann, H. (2013). Does logic feel good? Testing for intuitive detection of logicality in syllogistic reasoning. Journal of Experimental Psychology: Learning, Memory, and Cognition, 39(4), 1265-1273.
Morsanyi, K., & Handley, S. J. (2012). Logic feels so good-I like it! Evidence for intuitive detection of logicality in syllogistic reasoning. Journal of Experimental Psychology: Learning, Memory, and Cognition, 38(3), 596-616. 041b061a72