### Table 3: Natural deduction rules for classical connectives.

2000

"... In PAGE 16: ... This specialised version requires that in each of these rules the labels 1, 2 and 3 areallthesame. The set of rules for the _ and ^ classical connectives is given in Table3 , together with a special rule called ISub.TheISub expresses a speci c form of interaction between the R-literals constructed from the = predicate and the declarative units included in a con guration.... ..."

Cited by 1

### Table 1: Natural Deduction System for BI: NBI

2003

"... In PAGE 5: ...deduction system, as in Table1 , in which we use A0A3 , pronounced magic wand , for multiplicative impli- cation and A3, pronounced star , for multiplicative conjunction, AX and CM for their additive counterparts, and CN for disjunction. The units of A3, CM and CN are denoted C1, BQ and BR (inconsistency), respectively.... ..."

Cited by 17

### Table 4: Natural deduction rules for modal operators.

2000

Cited by 1

### Table 3. Deduction rules of prBPA.

1999

"... In PAGE 5: .... t; s 2DP)t + s 2DP. By PR we denote the set of all static and dynamic processes, that is PR = SP [DP: Moreover, there is a bijection from D to DP. The operational semantics of prBPA is given by the term deduction system T =( prBPA;D) induced by the deduction rules shown in Table3 where a is a variable that ranges over the set A, and the probability distribution function as... In PAGE 13: ... The main idea for proposing a new axiom system is to nd an appropriate theory which does not have any extra operators. As it has been already mentioned, in order to obtain a complete axiom system of the term model determined by the deduction rules in Table3 and Table 7 the merge with memory operator has been added to ACP+ . We denote the new process algebra by ACP .... ..."

Cited by 25

### Table 1: Rules for deductions in equational logic

1994

"... In PAGE 4: ...y means of many-sorted equational logic. We assume that is inhabited, i.e. that there are closed terms of every sort S 2 S, otherwise unsound deductions would be possible (a closed term is a term without variables). The axioms and rules of inference of the equational theory determined by ( ; E) are listed in Table1 . Substitutions are de ned as usual.... In PAGE 27: ... This can be easily veri ed by inspecting the eq function for natural numbers. The total set of equations that has to be considered is ENat = fNat1; : : : ; Nat8g [ fMod1; : : : ; Mod4g [ fQueue22; Queue23g [ f Table1 3; Table14g [ fBag14; Bag15g [ fSet21; Set22g: Note that for such a proof we need consistent speci cations for the sorts Bool, Queue, Table, Bag, and Set. To actually prove that 0 = Sn cannot be derived from ENat, term rewriting techniques can be used.... ..."

Cited by 3

### Table 2: The 14 derivation schemas used with the natural deduction networks.

1994

"... In PAGE 14: ... In this way, the simulation explores the strategy of dividing labor between external structured representations and a pattern-recognizing connectionist system. The natural deductions used by the network followed fourteen derivation patterns ( Table2 ). These derivation patterns involved derivations using either three or four premises and either three, four, or five inferential steps.... In PAGE 15: ... These totaled 252. - - - - - - - - - - - - - - - - - - - - - - - Insert Table2 about here - - - - - - - - - - - - - - - - - - - - - - - A feedforward connectionist network with one layer of hidden units was used for the simulation (Figure 2). The input layer consisted of 104 units, each of which received an activation of 0 or 1.... In PAGE 23: ... This objection was in fact raised by John Nolt in response to an early simulation with this network. In that simulation, only the first six argument forms from Table2 were employed, and the premises were only presented in the order given. Nolt constructed an alternative set of three principles that could account for success on these problems, relying not on principles of logic, but on the position of particular statements in the premises.... ..."

Cited by 1

### Table 2n3a Natural deduction rules and term assignment for linear logic.

1995

"... In PAGE 12: ... Thusn2c if the free variables of M are x 1 n3b n3a n3a n3an3b x n n2c then n28store Mn29 is shorthand for the expression n28store M where x 1 n3d x 1 n3b n3a n3a n3an3b x n n3d x n n29. The typing rules for the language appear in Table2 n2c where the symbols n00 and n01 denote type assignmentsn2c which are lists of pairs x 1 n3a s 1 n3b n3a n3a n3an3b x n n3a s n n2c where each x i is a distinct variable and each s i is a type. Each of the rules is built on the... ..."

### Table 1. R-deductive system for the standard syntax

1996

"... In PAGE 5: ... In other words, we only consider fully applied algebraic terms. In order to provide a uniform framework to specify and compare the systems used in the literature, the rules for derivation, in Table1 , are parametrised by a binary relation R on pseudo-terms. For lack of space, only one deductive system ` is considered here.... ..."

Cited by 3

### Table 3. Natural Semantics

2001

"... In PAGE 8: ...trees in natural semantics, in contrast to SOS. The usual style is to exhibit the environment as an extra argument to the evaluation relation, as illustrated in Table3 ; the resemblance to sequents in Gentzen calculi for Natural Deduction led to the name of the framework. a3 Evaluations are specified by axioms and inference rules.... ..."

Cited by 1