THE FIRST-ORDER LOGIC OF CZF IS INTUITIONISTIC FIRST-ORDER LOGIC

Intuitionistic Completeness of First-Order Logic

We establish completeness for intuitionistic first-order logic, iFOL, showing that a formula is provable if and only if its embedding into minimal logic, mFOL, is uniformly valid under the Brouwer Heyting Kolmogorov (BHK) semantics, the intended semantics of iFOL and mFOL. Our proof is intuitionistic and provides an effective procedure Prf that converts uniform minimal evidence into a formal fi...

On the Mints Hierarchy in First-Order Intuitionistic Logic

We stratify intuitionistic first-order logic over (∀,→) into fragments determined by the alternation of positive and negative occurrences of quantifiers (Mints hierarchy). We study the decidability and complexity of these fragments. We prove that even the ∆2 level is undecidable and that Σ1 is Expspace-complete. We also prove that the arity-bounded fragment of Σ1 is complete for co-Nexptime.

Hybrid Logic is the Bounded Fragment of First Order Logic

Hybrid languages are extended modal languages which can refer to (or even quantify over) worlds. The use of strong hybrid languages dates back to at least [Pri67], but recent work (for example [BS98, BT99]) has focussed on a more constrained system called H(↓,@). The purpose of the present paper is to show in detail thatH(↓,@) is a modally natural system. We study its expressivity, and provide ...

Hybrid Logic Is the Bounded Fragment of First Order Logic

Hybrid languages are extended modal languages which can refer to (or even quantify over) worlds. The use of strong hybrid languages dates back to at least Pri67], but recent work (for example BS98, BT99]) has focussed on a more constrained system called H(#; @). The purpose of the present paper is to show in detail that H(#; @) is a modally natural system. We study its expressivity, and provide...

First-Order Logic