Asadollah Fallahi

• Doctor of Philosophy
• Professor at Iranian Institute of Philosophy

We exhibit infinitely many semisimple varieties of semilinear De Morgan monoids (and likewise relevant algebras) that are not tabular, but which have only tabular proper subvarieties. Thus, the extension of relevance logic by the axiom $$(p\rightarrow q)\vee (q\rightarrow p)$$ ( p → q ) ∨ ( q → p ) has infinitely many pretabular axiomatic extension...

The international conference on the History of Logic in the Islamic World will be held between March 6-8, 2023 by the logic group at the Iranian Institute of Philosophy (IRIP) in collaboration with the Iranian Association for Logic (IAL), Iranian Philosophical Society (IPS), Institute for Interdisciplinary Research in Fundamental Sciences (IRFS), a...

The logical rule of contraposition as applied to a particular affirmative proposition (I-contraposition), despite its rejection in the medieval Latin logic, had a different history in the medieval Arabic logic, varying from common acknowledgement to total dismissal (it was accepted by Avicenna and by all of his followers in the eleventh and twelfth...

Recently, in ‘An inquiry on Fakhr al-Dīn Rāzī’s authorship of Al-manṭiq al-kabι¯r (MS Aḥmad iii, no. 3401)’, we refuted the quite common view among historians of Arabic logic as to attribute Al-manṭiq al-kabι¯r (Major [book on] logic) to Fakhr al-dīn Rāzī; however, in that paper, we could not identify the real author of the book. In this paper, we...

Pretabularity is the attribute of logics that are not characterised by finite matrices, but all of whose proper extensions are. Two of the first-known pretabular logics were Dummett’s famous super-intuitionistic logic LC and the well-known semi-relevance logic RM (= R-Mingle). In this paper, we investigate Anderson and Belnap’s relevance logic R wi...

It is quite common among historians of Arabic logic to attribute MS Aḥmad iii, no. 3401, entitled Al-manṭiq al-kabīr (Major [book on] logic), to Fakhr al-Dīn Rāzī. This view is expressed explicitly and forcefully by Franziska Knobel (2015) and Turgut Akyüz and Elmin Aliyev (2020). In this paper, we try to refute this attribution through textual ana...

KR is Anderson and Belnap’s relevance logic R with the addition of the axiom of EFQ: \( (p \,\, \& \sim p) \rightarrow q\). Since KR is relevantistic as to implication but classical as to negation, it has been dubbed, among many others, a ‘classical relevance logic.’ For KR, there have been known so far just two pretabular normal extensions. For th...

The rule of contraposition has been investigated thoroughly by Arabic logicians. In this paper, we study the work done by Fārābā and Avicenna, the fathers of Arabic logic. Fārābā studied contraposition of universal affirmatives, discussed its four forms, and discovered a relation between one form and the conversion of negative universals. Although...

Pretabular logics are those that lack finite characteristic matrices, although all of their normal proper extensions do have some finite characteristic matrix. Although for Anderson and Belnap’s relevance logic R, there exists an uncountable set of pretabular extensions (Swirydowicz in J Symb Log 73(4):1249–1270, 2008), for the classical relevance...