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In this paper, we develop techniques for automated hypothesis-space exploration over data sets that may contain contradictions. To do so, we make use of the equivalence between two formulations: those of first-order predicate logic with prefix modal quantifiers under the finite-model hypothesis and those of mixed-integer linear programming (MILP) problems. Unlike other approaches, we do not assume...
We study the complexity of evaluating positive equality-free sentences of first-order (FO) logic over a fixed, finite structure B. This may be seen as a natural generalisation of the non-uniform quantified constraint satisfaction problem QCSP(B). We introduce subjective hyper-endomorphisms and use them in proving a Galois connection that characterises definability in positive equality-free FO. Through...
In the work of Nash et al. (2005) have raised the question whether a logic Lles, already introduced by Gurevich in 1988, captures polynomial time, and they give a reformulation of this question in terms of a parameterized halting problem p-Accles for nondeterministic Turing machines. We analyze the precise relationship between Lles and p-Accles. We show that p-Accles is not fixed-parameter tractable...
A principle directly pertinent to feasibility, which justifies the identification of P-time with feasible computing, is proposed. It is shown that the computable functions justified on the basis of positive quantifier-free comprehension are precisely the functions computable in deterministic polynomial time. This shows that the class P-time arises naturally from a foundational analysis of feasibility,...
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