Two algebraic structures, the contrapositionally complemented Heyting algebra (ccHa) and the contrapositionally |$\vee $| complemented Heyting algebra (c|$\vee $|cHa), are studied. The salient feature of these algebras is that there are two negations, one intuitionistic and another minimal in nature, along with a condition connecting the two operators. Properties of these algebras are discussed, examples are given and comparisons are made with relevant algebras. Intuitionistic Logic with Minimal Negation (ILM) corresponding to ccHas and its extension |${\textrm {ILM}}$|-|${\vee }$| for c|$\vee (...) $|cHas are then investigated. Besides its relations with intuitionistic and minimal logics, ILM is observed to be related to Peirce’s logic and Vakarelov’s logic MIN. With a focus on properties of the two negations, relational semantics for ILM and |${\textrm {ILM}}$|-|${\vee }$| are obtained with respect to four classes of frames, and inter-translations between the classes preserving truth and validity are provided. ILM and |${\textrm {ILM}}$|-|${\vee }$| are shown to have the finite model property with respect to these classes of frames and proved to be decidable. Extracting features of the two negations in the algebras, a further investigation is made, following logical studies of negations that define the operators independently of the binary operator of implication. Using Dunn’s logical framework for the purpose, two logics |$K_{im}$| and |$K_{im-{\vee }}$| are discussed, where the language does not include implication. The |$K_{im}$|-algebras are reducts of ccHas and are different from relevant algebraic structures having two negations. The negations in the |$K_{im}$|-algebras and |$K_{im-{\vee }}$|-algebras are shown to occupy distinct positions in an enhanced form of Dunn’s kite of negations. Relational semantics for |$K_{im}$| and |$K_{im-{\vee }}$| is provided by a class of frames that are based on Dunn’s compatibility frames. It is observed that this class coincides with one of the four classes giving the relational semantics for ILM and |${\textrm {ILM}}$|-|${\vee }$|⁠. (shrink)

In an oft-quoted letter, King James IV wrote to the Dominican Prior General that Scotland was "almost the most remote region in the world."1 Nevertheless, as scholarship of the past fifteen years has shown, later medieval Scotland played a central role in Latin Christendom.2 Perhaps most importantly for the current study, numerous religious orders were active in Scotland and had significant ties to the Continent.3 Many of the same questions pertaining to Continental houses also exist for Scotland. In particular, there (...) are many unanswered questions about the group known as the Franciscan third order. Sources indicate that there were a number of men and women known as... (shrink)

Traditional Franciscan history holds that Francis of Assisi founded an order of lay penitents, which was given both a rule and official approval by Pope Nicholas IV in 1289. In this accepted version of events, the 1289 rule was followed by houses of men and women until the sixteenth century, and only replaced when a desire for greater unity within the Franciscan third order led Leo X to issue a new rule in 1521.2 Despite not standing up to historical scrutiny, (...) studies of the third order seldom question this official narrative.3 Moreover, although the 1521 rule is generally mentioned, little attention is given to either its context or significance.4 When the historical circumstances of this new rule are .. (shrink)