We propose a notion of $o$-minimality for partially ordered structures. Then we study $o$-minimal partially ordered structures $(A, \leq, \ldots)$ such that $(A,\leq)$ is a Boolean algebra. We prove that they admit prime models over arbitrary subsets and we characterize $\omega$-categoricity in their setting. Finally, we classify $o$-minimal Boolean algebras as well as $o$-minimal measure spaces.

We propose a combination of Bochvar's strict three-valued logic, McCarthy's sequential three-valued logic, and process algebra via the conditional guard construct. This combination entails the introduction of a new constant meaningless in process algebra. We present an operational semantics in SOS-style, and a completeness result for ACP with conditional guard construct and the proposed logic.

In this paper we prove the uncompactness of every stit logic that contains a generalized refref conditional and is a sublogic of the stit logic with refref equivalence, a syntactical condition of uncompactness that covers infinitely many stit logics. This result is established through the uncompactness of every stit logic whose semantic structures contain no chain of busy choice sequences with cardinality $n$, where $n$ is any natural number $ > 0$. The basic idea in the proof is to apply the notion of companions to stit sentences in finding busy choice sequences in structures, and to make use of a relation between chains of busy choice sequences and generalized refref conditionals in connecting the two conditions of uncompactness mentioned above.

This paper presents an example of a supersimple nonlow theory and characterizes its independence relation.

A linear order is $n$-decidable if its universe is $\mathbb{N}$ and the relations defined by $\Sigma_{n}$ formulas are uniformly computable. This means that there is a computable procedure which, when applied to a $\Sigma_{n}$ formula $\varphi(\bar{x})$ and a sequence $\bar{a}$ of elements of the linear order, will determine whether or not $\varphi(\bar{a})$ is true in the structure. A linear order is decidable if the relations defined by all formulas are uniformly computable.

These definitions suggest two questions. Are there, for each $n$, $n$-decidable linear orders that are not $(n+1)$-decidable? Are there linear orders that are $n$-decidable for all $n$ but not decidable? The former was answered in the positive by Moses in 1993. Here we answer the latter, also positively.

We show that if $T$ is a stable theory with ndop and ndidip, then $\vert T\vert^{+}$-primary models over free trees are $\vert T\vert^{+}$-minimal over the tree. As a corollary we show, for example, that if $T$ is a stable theory and for all nonempty $X$, $acl(X)=\cup_{x\in X}acl(\{ x\} )$, then $T$ is superstable or it has dop or didip.

We show that Pitts' modeling of propositional quantification in intuitionistic logic (as the appropriate interpolants) does not coincide with the topological interpretation. This contrasts with the case of the monadic language and the interpretation over sufficiently regular topological spaces. We also point to the difference between the topological interpretation over sufficiently regular spaces and the interpretation of propositional quantifiers in Kripke models.

We generalize an observation made by Goldblatt in "Diodorean modality in Minkowski spacetime" by proving that each $n$-dimensional integral spacetime frame equipped with Robb's irreflexive `after' relation determines a unique temporal logic. Our main result is that, unlike $n$-dimensional spacetime where, as Goldblatt has shown, the Diodorean modal logic is the same for each frame $(\mathbb{R}^{n}, \leq)$, in the case of $n$-dimensional integral spacetime, the frame $(\mathbb{Z}^{n},\leq)$ determines a unique Diodorean modal logic.

Aristotle's modal syllogistic has been described as "incoherent," "a failure," "a realm of darkness." Even the gentler critics claim that it is inconsistent. I offer an interpretation according to which validity in the modal syllogistic is always obtained by substituting modal terms in the nonmodal syllogistic, and restricting the principles of modal conversion. In this paper I discuss the apodeictic syllogistic, showing that the restrictions I propose are powerful enough to do all the work Aristotle requires and, in fact, are supported by a close analysis of Aristotle's text. The upshot of this is that there is for Aristotle no separate modal syllogistic.

In Volume 33:1 of the Notre Dame Journal of Formal Logic, a system for diagramming syllogistic inferences using straight line segments is presented by Englebretsen. In light of recent research on the representational power of diagrammatic representation systems by the authors, we point out some problems with the proposal, and indeed, with any proposal for representing logically possible situations diagrammatically. We shall first outline the proposed linear diagrammatic system of Englebretsen, and then show by means of counterexamples that it is inadequate as a representation scheme for general logical inferences (the task for which the system is intended). We also show that modifications to the system fail to remedy the problems. The considerations we present are not limited to the particular proposal of Englebretsen; we thus draw a more general moral about the use of spatial relations in representation systems.

Mario Savio is widely known as the first spokesman for the Free Speech Movement. Having spent the summer of 1964 as a civil rights worker in segregationist Mississippi, Savio returned to the University of California at a time when students throughout the country were beginning to mobilize in support of racial justice and against the deepening American involvement in Vietnam. His moral clairty, his eloquence, and his democratic style of leadership inspired thousands of fellow Berkeley students to protest university regulations that had severely limited political speech and activity on campus. The nonviolent campaign culminated in the largest mass arrest in American history, drew widespread faculty support, and resulted in a revision of university rules to permit political speech and organizing. This significant advance for student freedom rapidly spread to countless other colleges and universities across the country. Mario Savio went on to become a college teacher of physics, logic, and philosophy, to speak and organize in favor of immigrant rights and affirmative action and against U.S. intervention in Central America. He died on November 6, 1996, in the middle of a struggle against California State University fee hikes that hurt working-class students. Savio had submitted this article to the Notre Dame Journal of Formal Logic before he died. Final revisions were made by Philip Clayton with the assistance of Mario's colleagues at Sonoma State University. As reader for the Journal, George Englebretsen not only provided an extensive commentary on the article--much of which has been incorporated here--but also assisted in the difficult task of making revisions without changing the substance of Mario's style or thought. It is fitting that this, Savio's final publication, would be pedagogical in orientation. For him, moral considerations were no less pertinent in logic than in philosophy's less abstract fields. The usual student confusion with Venn diagrams led him to develop the new pictorial device presented in the following pages, which he believed was more sensitive to user psychology. It is hard to miss the political overtones in Savio's closing worry that in Venn diagrams "information of real significance may occasionally appear hidden and distorted." The decision by the Notre Dame Journal of Formal Logic to publish this piece posthumously is a testimony that logic, no less than other fields of philosophy, can be a tool of free speech and political change--as powerful in its way as the rhetorical brilliance of that young man standing on top of a police car who launched a worldwide movement with the words, "There is a time when the operation of the machine becomes so odious, makes you so sick at heart, you can't take part."