Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

Discrete Tense Logic with Infinitary Inference Rules and Systematic Frame Constants: A Hilbert-Style Axiomatization

Lennart Äqvist
Journal of Philosophical Logic
Vol. 25, No. 1 (Feb., 1996), pp. 45-100
Published by: Springer
Stable URL: http://www.jstor.org/stable/30227089
Page Count: 56
  • Download ($43.95)
  • Cite this Item
Discrete Tense Logic with Infinitary Inference Rules and Systematic Frame Constants: A Hilbert-Style Axiomatization
Preview not available

Abstract

The paper deals with the problem of axiomatizing a system T1 of discrete tense logic, where one thinks of time as the set Z of all the integers together with the operations +1 ("immediate successor") and-1 ("immediate predecessor"). T1 is like the Segerberg-Sundholm system WI in working with so-called infinitary inference ruldes; on the other hand, it differs from W I with respect to (i) proof-theoretical setting, (ii) presence of past tense operators and a "now" operator, and, most importantly, with respect to (iii) the presence in T1 of so-called systematic frame constants, which are meant to hold at exactly one point in a temporal structure and to enable us to express the irreflexivity of such structures. Those frame constants will be seen to play a paramount role in our axiomatization of T1.

Page Thumbnails

  • Thumbnail: Page 
[45]
    [45]
  • Thumbnail: Page 
46
    46
  • Thumbnail: Page 
47
    47
  • Thumbnail: Page 
48
    48
  • Thumbnail: Page 
49
    49
  • Thumbnail: Page 
50
    50
  • Thumbnail: Page 
51
    51
  • Thumbnail: Page 
52
    52
  • Thumbnail: Page 
53
    53
  • Thumbnail: Page 
54
    54
  • Thumbnail: Page 
55
    55
  • Thumbnail: Page 
56
    56
  • Thumbnail: Page 
57
    57
  • Thumbnail: Page 
58
    58
  • Thumbnail: Page 
59
    59
  • Thumbnail: Page 
60
    60
  • Thumbnail: Page 
61
    61
  • Thumbnail: Page 
62
    62
  • Thumbnail: Page 
63
    63
  • Thumbnail: Page 
64
    64
  • Thumbnail: Page 
65
    65
  • Thumbnail: Page 
66
    66
  • Thumbnail: Page 
67
    67
  • Thumbnail: Page 
68
    68
  • Thumbnail: Page 
69
    69
  • Thumbnail: Page 
70
    70
  • Thumbnail: Page 
71
    71
  • Thumbnail: Page 
72
    72
  • Thumbnail: Page 
73
    73
  • Thumbnail: Page 
74
    74
  • Thumbnail: Page 
75
    75
  • Thumbnail: Page 
76
    76
  • Thumbnail: Page 
77
    77
  • Thumbnail: Page 
78
    78
  • Thumbnail: Page 
79
    79
  • Thumbnail: Page 
80
    80
  • Thumbnail: Page 
81
    81
  • Thumbnail: Page 
82
    82
  • Thumbnail: Page 
83
    83
  • Thumbnail: Page 
84
    84
  • Thumbnail: Page 
85
    85
  • Thumbnail: Page 
86
    86
  • Thumbnail: Page 
87
    87
  • Thumbnail: Page 
88
    88
  • Thumbnail: Page 
89
    89
  • Thumbnail: Page 
90
    90
  • Thumbnail: Page 
91
    91
  • Thumbnail: Page 
92
    92
  • Thumbnail: Page 
93
    93
  • Thumbnail: Page 
94
    94
  • Thumbnail: Page 
95
    95
  • Thumbnail: Page 
96
    96
  • Thumbnail: Page 
97
    97
  • Thumbnail: Page 
98
    98
  • Thumbnail: Page 
99
    99
  • Thumbnail: Page 
100
    100