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This paper combines two classes of generalized logics, one of which is the class of weakly implicative logics introduced by Cintula and the other of which is the class of gaggle logics introduced by Dunn. For this purpose we introduce implicational tonoid logics. More precisely, we first define implicational tonoid logics in general and examine their relation to weakly implicative logics. We then provide algebraic semantics for implicational tonoid logics. Finally, we consider relational semantics, called Routley–Meyer–style semantics, for finitary those logics.

Urquhart works in several areas of logic where he has proved important results. Our paper outlines his topological lattice representation and attempts to relate it to other lattice representations. We show that there are different ways to generalize Priestley's representation of distributive lattices---Urquhart's being one of them, which tries to keep prime filters (or their generalizations) in the representation. Along the way, we also mention how semilattices and lattices figured into Urquhart's work.

This paper considers modalities added to the relevance logic LR (lattice-R), which is R with the distributivity of conjunction and disjunction omitted. First, the modalities are defined from the Ackermann constants and the lattice connectives. Then, we introduce modalities as primitives equipped with some fairly usual properties. We also consider some other logics in the neighborhood. For each logic, including classical linear logic, we prove decidability. Lincoln, Mitchell, Scedrov, and Shankar (1992) claimed to have proved classical linear logic undecidable. We examine their work and find that their paper does not contain a proof of the admissibility of the cut rule, which would be essential for their claims to hold. Furthermore, according to their interpretation of proofs in linear logic, computations that lead to a dead-end state are not considered, unlike computations from inaccessible states that are included. The same problem with the direction of a proof vs the direction of a computation appears in all other publications that claim undecidability, including Kanovich (2016).

Urquhart works in several areas of logic where he has proved important results. Our paper outlines his topological lattice representation and attempts to relate it to other lattice representations. We show that there are different ways to generalize Priestley’s representation of distributive lattices—Urquhart’s being one of them, which tries to keep prime filters (or their generalizations) in the representation. Along the way, we also mention how semi-lattices and lattices figured into Urquhart’s work.

Arnon Avron has written: “Dunn-McCall logic RM is by far the best understood and the most well-behaved in the family of logics developed by the school of Anderson and Belnap.” I agree. There is the famous saying: “Do not let the perfect become the enemy of the good.” I might say: “good enough.” In this spirit, I will examine the logic R-Mingle, exploring how (in the terminology of Avron) it is only a “semi-relevant logic” but still a paraconsistent logic. I shall discuss the history of RM, and compare RM to Anderson and Belnap’s system R of relevant implication and to classical two-valued logic. There is a “consumer’s guide,” evaluating these logics as “tools,” in the light of my recent work on “Humans as Rational Toolmaking Animals.”

In this chapter, we are interested in understanding the nature of information and its value. We focus on information that is used for making decisions, including related activities such as constructing models, performing inferences, and making predictions. Our discussion is mostly qualitative, and it touches on certain aspects of information as related to the sender, receiver, and a possible observer. Although our emphasis is on shedding more light on the concept of information for making decisions, we are not concerned here with the exact details of the decision process, or information processing itself. In addition to discussing information, our expedition takes us through the traditional notions of utility, prices, and risk, all of which, under certain conditions, relate to the value of information. Our main conclusion is that the value of information (used in decision making) is relative and subjective. Since information is relative, it can have more than one value, say a value for the sender, a value for the receiver, or even different values for different senders and receivers, and various values for various “eavesdroppers.” Of course, the value might be zero for any of these. Importantly, that value is inversely related to risk when the information is used for decision making. Although this conclusion is likely expected, we did argue for it in a way that relies on some fundamentals about both value and information.