Towards a proof theory for Henkin quantifiers

Author(s):  
Matthias Baaz ◽  
Anela Lolic

Abstract This paper presents a methodology to construct globally sound but possibly locally unsound analytic calculi for partial theories of Henkin quantifiers. It is demonstrated that usual locally sound analytic calculi do not exist for any reasonable fragment of the full theory of Henkin quantifiers. This is due to the combination of strong and weak quantifier inferences in one quantifier rule.

Author(s):  
Sara Negri ◽  
Jan von Plato ◽  
Aarne Ranta

Author(s):  
A. S. Troelstra ◽  
H. Schwichtenberg
Keyword(s):  

Author(s):  
J. R. B. Cockett ◽  
R. A. G. Seely

This chapter describes the categorical proof theory of the cut rule, a very basic component of any sequent-style presentation of a logic, assuming a minimum of structural rules and connectives, in fact, starting with none. It is shown how logical features can be added to this basic logic in a modular fashion, at each stage showing the appropriate corresponding categorical semantics of the proof theory, starting with multicategories, and moving to linearly distributive categories and *-autonomous categories. A key tool is the use of graphical representations of proofs (“proof circuits”) to represent formal derivations in these logics. This is a powerful symbolism, which on the one hand is a formal mathematical language, but crucially, at the same time, has an intuitive graphical representation.


Author(s):  
James Manwaring

AbstractMany philosophers have raised difficulties for any attempt to proportion punishment severity to crime seriousness. One reason for this may be that offering a full theory of proportionality is simply too ambitious. I suggest a more modest project: setting a lower bound on proportionate punishment. That is, I suggest a metric to measure when punishment is not disproportionately severe. I claim that punishment is not disproportionately severe if it imposes costs on a criminal wrongdoer which are no greater than the costs which they intentionally caused to others. I flesh out the implications of this Lower bound by discussing how to measure the costs of crime. Methodologically, I claim that different costs should be compared by considering preferences. Substantively, I claim that many proportionality judgements undercount the costs of crime by focusing only on the marginal and not the average cost. I suggest that we may hold defendants causally responsible for their contribution to the costs of that type of crime.


1987 ◽  
Vol 10 (4) ◽  
pp. 387-413
Author(s):  
Irène Guessarian

This paper recalls some fixpoint theorems in ordered algebraic structures and surveys some ways in which these theorems are applied in computer science. We describe via examples three main types of applications: in semantics and proof theory, in logic programming and in deductive data bases.


2020 ◽  
Vol 21 (4) ◽  
pp. 1-31
Author(s):  
Liron Cohen ◽  
Reuben N. S. Rowe

Religions ◽  
2021 ◽  
Vol 12 (8) ◽  
pp. 613
Author(s):  
Christopher Tollefsen

Critics of the “New” Natural Law (NNL) theory have raised questions about the role of the divine in that theory. This paper considers that role in regard to its account of human rights: can the NNL account of human rights be sustained without a more or less explicit advertence to “the question of God’s existence or nature or will”? It might seem that Finnis’s “elaborate sketch” includes a full theory of human rights even prior to the introduction of his reflections on the divine in the concluding chapter of Natural Law and Natural Rights. But in this essay, I argue that an adequate account of human rights cannot, in fact, be sustained without some role for God’s creative activity in two dimensions, the ontological and the motivational. These dimensions must be distinguished from the epistemological dimension of human rights, that is, the question of whether epistemological access to truths about human rights is possible without reference to God’s existence, nature, or will. The NNL view is that such access is possible. However, I will argue, the epistemological cannot be entirely cabined off from the relevant ontological and motivational issues and the NNL framework can accommodate this fact without difficulty.


Author(s):  
Heda Festini

With the analysis of the key terms such as truth/use, proof - verification, falsification, inductive probability/semantic probability, winning/losing, winning strategy, it is shown that Dummett’s general theory of meaning does not include Hintikka’s game theory, that it, the conception of the winning strategy. The difference between them arises from the different understanding of Wittgenstein's idea about language games and from their attitudes toward theoretical proof theory. Hintikka’s semantic games about exploration of the world do not reject the bivalence principle but he gives it a different characteristic - one of the two players always has a winning strategy. Looking at Dummett’s philosophical theory of meaning and the most recent Hintikka’s suggestion about general information - seeking through questioning and answering, the author establishes that Dummett’s falsificational and dialogical games as well as Hintikka’s semantic games are subparts of Hintikka’s general information - seeking game Thus Dummett’s statement that Hintikka’s semantic games can be subsumed under Dummett’s conception is rejected and thus the answer is partly given to Saarinen’s suggestion that new affinity should be established. Apart from the comparison of these views with the outline of possible Wittgenstein’s general theory of meaning as rule - testing, together with his treatment (although not always adequate) of verification/falsification, inductive probability and čonfirmation/corroboration, the advantage of Wittgenstein’s view is affirmed.


Sign in / Sign up

Export Citation Format

Share Document