### Abstract

This master thesis examines the distinction between tense logic

and first order logic concerning time. In particular it studies

whether this distinction exists in physics or not.

Firstly a general test is made: translating sentences concern-

ing time from physics into the two logics. The results here are

inconclusive, as it is possible for both logics to represent the sen-

tences, so this experiment does not reveal a similar distinction

in physics. However this test also reveals some properties of the

logics: tense logic holds a local view on time while first order logic

holds a global view, and it is possible to translate tense logical

formulas into first order logic with the standard translation.

Secondly it is examined whether properties of reversibility in

physics can be compared with properties of the two logics; this

is done under the conjecture that there is a correspondence be-

tween first order logic and reversibility in physics and tense logic

and irreversibility in physics. Through this study it is concluded

that it is not possible to see this correspondence with the tested

property; time symmetry, since symmetry seems to concern the

underlying structures, not the logic itself. It is, on the other hand,

possible to see the correspondence while looking at the property

of being fundamental. Through a presentation of Onsager's re-

ciprocal relation, reversibility is shown to be fundamental. In

logic, fundamentality of first order logic is argued for through the

standard translation.

Finally it is noted that the finite model property and the decid-

ability of tense logic gives useful properties that the more funda-

mental first order logic has not.

It is concluded that it is unclear whether the distinction of time

between the two logics exists in physics.

and first order logic concerning time. In particular it studies

whether this distinction exists in physics or not.

Firstly a general test is made: translating sentences concern-

ing time from physics into the two logics. The results here are

inconclusive, as it is possible for both logics to represent the sen-

tences, so this experiment does not reveal a similar distinction

in physics. However this test also reveals some properties of the

logics: tense logic holds a local view on time while first order logic

holds a global view, and it is possible to translate tense logical

formulas into first order logic with the standard translation.

Secondly it is examined whether properties of reversibility in

physics can be compared with properties of the two logics; this

is done under the conjecture that there is a correspondence be-

tween first order logic and reversibility in physics and tense logic

and irreversibility in physics. Through this study it is concluded

that it is not possible to see this correspondence with the tested

property; time symmetry, since symmetry seems to concern the

underlying structures, not the logic itself. It is, on the other hand,

possible to see the correspondence while looking at the property

of being fundamental. Through a presentation of Onsager's re-

ciprocal relation, reversibility is shown to be fundamental. In

logic, fundamentality of first order logic is argued for through the

standard translation.

Finally it is noted that the finite model property and the decid-

ability of tense logic gives useful properties that the more funda-

mental first order logic has not.

It is concluded that it is unclear whether the distinction of time

between the two logics exists in physics.

Original language | English |
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Place of Publication | Roskilde |
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Publisher | Roskilde Universitet |

Number of pages | 64 |

Publication status | Published - Nov 2017 |

Series | Tekster fra IMFUFA |
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Number | 506 |

ISSN | 0106-6242 |

## Cite this

Kofod, J. L. (2017).

*A Dialogue on Time: Two Logics of Time and Physics*. Roskilde Universitet. Tekster fra IMFUFA, No. 506 http://milne.ruc.dk/imfufatekster/pdf/506.pdf