## A Cut-free Sequent Calculus for Elementary Situated Reasoning (1991)

Citations: | 10 - 3 self |

### BibTeX

@TECHREPORT{Seligman91acut-free,

author = {Jerry Seligman},

title = {A Cut-free Sequent Calculus for Elementary Situated Reasoning},

institution = {},

year = {1991}

}

### OpenURL

### Abstract

A rst-order language is interpreted in the following way: terms are regarded as referring to situations and the truth of formulae is relativized to a situation. The language is then extended to include formulae of the form t : (where t is a term and is a formula) meaning that is true in the situation referred to by t. Gentzen's sequent calculus for classical rst-order logic is extended with rules which capture this interpretation. Variants of the calculus and extensions of the language are discussed and the Cut rule is shown to be eliminable from some of the proposed calculi. Situation theory has been concerned with a range of issues centring around the partiality, context dependency and intensional structure of information. In formalizing situation theory one must focus on a specic aspect of the whole package | there is too much uncertainty and equivocation about the connections between the various parts. A dominant approach in recent years has been to focus on build...

### Citations

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(Show Context)
Citation Context ...and variable domains within the context of situation theory. There is, of course, a precedent for the cumulative-domain approach in Barwise's writings about the `part-of' relation between situations (=-=Barwise 1989-=-). Pursuing the connection withsrst-order modal logic further, we note that all our terms are acting like rigid designators. This is another assumption which needs to be questioned: perhaps a systemat... |

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Citation Context ... In keeping with the tradition of the Proof Theorists we think of the meaning of the supports relation as being given by its introduction and elimination rules within a calculus of natural deduction (=-=Prawitz 196-=-5). The introduction rule can be found by asking on what premises the situated reasoner can rationally conclude that s j= . Similarly, the elimination rule is found by asking what 2 she can rationally... |

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(Show Context)
Citation Context ...rent situation, the information that s holds just in case the current situation is s. The study of logics with terms occurring as formulae is of current interest in theselds of modal and tense logic (=-=Blackburn 1990-=-, Gargov & Goranko 1991) and feature logic (Reape 1991). In the modal case there is little change in the standard possible-world semantics of these languages | terms are regarded as formulae which are... |

18 |
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(Show Context)
Citation Context ...rporate. Perspectives. The ability of these languages to say that a situation supports information of the form s : allows a partial formalization of the notion of a perspective in situation theory (S=-=eligma-=-n 1989,1990a). In L 0 , for example, relative to a theory , each term t denes a classication C t of situation (terms) by formulae: s is classied in C t as being of type i the sequent ` t : (s : ) is ... |

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(Show Context)
Citation Context ...f of a sequent ` is a subformula of a formula in or . In other words, the logic (classical propositional logic, in this case) obeys a principle of \purity of methods" (Girard 1987) or is analyti=-=c (Smullyan 1968-=-, Fitting 1983); the possible proofs of a sequent being determined entirely by its parts. 6 To this extremely elegant calculus, we add new rules to re ect the principles of situated reasoning outlined... |

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(Show Context)
Citation Context ...as been to focus on building models of various situation theoretic objects, usually in the universe of non-well-founded sets or in some other category of structured objects (Barwise 1987, Aczel 1990, =-=Fernando 198-=-9). The aim of this research | as I understand it | is to specify the mutual connections between identity criteria for the dierent kinds of entity about which situation theorists talk. Here we adopt a... |

6 |
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(Show Context)
Citation Context ...the current situation is s. The study of logics with terms occurring as formulae is of current interest in theselds of modal and tense logic (Blackburn 1990, Gargov & Goranko 1991) and feature logic (=-=Reape 1991-=-). In the modal case there is little change in the standard possible-world semantics of these languages | terms are regarded as formulae which are true at exactly one world | but there is an appreciab... |

1 |
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(Show Context)
Citation Context ...approach in recent years has been to focus on building models of various situation theoretic objects, usually in the universe of non-well-founded sets or in some other category of structured objects (=-=Barwise 198-=-7, Aczel 1990, Fernando 1989). The aim of this research | as I understand it | is to specify the mutual connections between identity criteria for the dierent kinds of entity about which situation theo... |