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Koepke introduced a machine model of computation that uses infinite time and space. In our thesis, we generalize Koepke’s model by allowing for infinite programs in addition to infinite time and space. With this new model of computation, we prove generalizations of basic results from finite compu...
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A very general intuition about conditionals is that they ask us to consider their consequents in light of their antecedents. Different theories cash out this intuition in different ways, but one common assumption is that an agent parsing a conditional must consider only the ways in which the ante...
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In this thesis, the philosophical debate on conceptual relativism between Quine and Davidson is examined, along with their respective theories of interpretation. A new perspective on the issues raised by these philosophers in their theoretical accounts of linguistic comprehension is introduced th...
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We study abstract argumentation, argument based belief and their dynamics in the setting of Hybrid logic. For this purpose, we develop Hybrid Argumentation Logic (HAL), a logic optimized to express the concepts of abstract argumentation theory. Combining HAL, a theory of support between arguments...
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The standard semantics for counterfactuals, due to Lewis (1973) and Stalnaker (1968), defends that a counterfactual p ⇒ q is true if, and only if, q is true at all the closest possible worlds where p is true. This semantics predicts that all counterfactuals with metaphysically impossible antecede...
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In this thesis, I define the notion of inquisitive logical triviality, and investigate its connection to grammaticality in natural language. Inquisitive logical triviality is a property characterizing sentences which are either contradictory, or tautologous and non-inquisitive, purely in virtue o...
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In recent years interest has risen in combining knowledge representation and machine learning and in this thesis we explore Real Logic (RL). RL offers a novel approach to this combination. RL uses first-order logic (FOL) syntax and has a many-valued semantics in which terms are interpreted as rea...
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Focus particles like only, too, even, etc. are well studied expressions in formal semantics. They received a lot of attention from different view points, e.g. presupposition theory and the study of scalar implicatures. However, these particles did not receive as much attention when occurring in q...
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The increasing pervasiveness, autonomy and complexity of artificially intelligent technologies in human society has challenged the traditional conception of moral responsibility. To this extent, it has been proposed that the existing notion of moral responsibility be expanded in order to be able ...
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We present a formal system, ACT, that is used to express the time-complexity of computing functions. Every proof that can be made within the system relativizes. The system uses combinatory logic instead of Turing machines. We do show that it is invariant with respect to Turing machines.
We obtai...
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The Gibbard-Satterthwaite Theorem tells us that most voting rules are susceptible to strategic manipulation, which means that a voter can benefit from voting something other than their true preference. In this theorem, however, it is assumed that voters have full information about the preferences...