You signed in with another tab or window. Reload to refresh your session.You signed out in another tab or window. Reload to refresh your session.You switched accounts on another tab or window. Reload to refresh your session.Dismiss alert
@@ -98,11 +98,10 @@ For a given logic, there may be thousands of satisfiable matrix models. Finding
98
98
99
99
100
100
\\
101
-
<aname="shay"></a> **Nonuniform Substitutions, Variable Sharing, and the Enigma of Contraction**\\
102
-
Shay Logan (*Kansas State University*)
103
-
104
-
Relevant logics share variables. Weak relevant logics are also closed under interesting classes of nonuniform substitutions. In this talk I will show that in a range of interesting cases, the latter entails the former. This allows us give easy proofs of (new and exciting!) strong variable sharing results without relying on Belnap’s variable sharing results for the logic R. But there’s an enigma to address. R admits contraction. So variable sharing and contraction are clearly compatible. Yet (as I will show) contraction seems entirely incompatible with the whole business of nonuniform substitutions. If time permits after surveying this much, I will say a few
105
-
words about how we might overcome this obstacle.
101
+
<aname="shawn"></a> **The Significance of Variable-Sharing**\\
102
+
Shawn Standefer *(National Taiwan University)*
103
+
104
+
In previous work, I suggested that we can use variable-sharing to define the class of relevant logics. In this talk, I will expand on this idea and explore the significance of variable-sharing. The goal will be to identify some of its prominent philosophical consequences. I will also use it as a foil to help identify features of the usual suspects in the relevant logic literature, e.g. B, R, T, etc., that distinguish them as interesting and important logics.
106
105
107
106
108
107
\\
@@ -171,10 +170,11 @@ I'll end by suggesting that to combination of some form of hyperformality and th
171
170
172
171
173
172
\\
174
-
<aname="shawn"></a> **The Significance of Variable-Sharing**\\
175
-
Shawn Standefer *(National Taiwan University)*
176
-
177
-
In previous work, I suggested that we can use variable-sharing to define the class of relevant logics. In this talk, I will expand on this idea and explore the significance of variable-sharing. The goal will be to identify some of its prominent philosophical consequences. I will also use it as a foil to help identify features of the usual suspects in the relevant logic literature, e.g. B, R, T, etc., that distinguish them as interesting and important logics.
173
+
<aname="shay"></a> **Nonuniform Substitutions, Variable Sharing, and the Enigma of Contraction**\\
174
+
Shay Logan (*Kansas State University*)
175
+
176
+
Relevant logics share variables. Weak relevant logics are also closed under interesting classes of nonuniform substitutions. In this talk I will show that in a range of interesting cases, the latter entails the former. This allows us give easy proofs of (new and exciting!) strong variable sharing results without relying on Belnap’s variable sharing results for the logic R. But there’s an enigma to address. R admits contraction. So variable sharing and contraction are clearly compatible. Yet (as I will show) contraction seems entirely incompatible with the whole business of nonuniform substitutions. If time permits after surveying this much, I will say a few
0 commit comments